The Answer Depends Upon The Facts Of The Case Related To The Forum Where The Suit Is Commenced
The analysis depends upon some key facts that a person asking a question might not know, because they are not intuitively obvious and have actually changed in the last few years, without knowing the relevant law.
When The Forum State Has General Jurisdiction Over All Defendants
The most important question to consider is this one:
Is the state in which the class action suit is brought is home to the headquarters of the US manufacturer (or a state where the manufacturer has a substantial equivalent to a headquarters)?
This question matters because, if and only if the answer to this question is "yes" then, "general jurisdiction" would be present under a U.S. Supreme Court precedent established in 2014.
If a forum state's courts have "general jurisdiction" over a defendant, this means that the defendant can be sued in that forum on any cause of action against that defendant arising anywhere in the world, regardless of any other relationship that the claim has to the forum state (except for claims in the exclusive jurisdiction of the federal courts which can be brought in a U.S. District Court located in the same state, or in an arbitration forum pursuant to a valid arbitration clause that binds the parties, an issue beyond the scope of this question and answer).
Until recently general jurisdiction over a defendant (i.e. jurisdiction over any lawsuit against a defendant without regard to the particular facts of the case) was present in any state where a company has a permanent office for the conduct of business, under half a century of precedent on the issue that traced back to a U.S. Supreme Court case known as International Shoe v. State of Washington, 326 U.S. 310 (1945). In the case of large corporations doing business nationwide, this usually meant that a plaintiff had a large number of states to choose from in which a defendant could be sued on any matter whatsoever which also facilitated the filing of class action lawsuits with plaintiffs from all over the world covered by a single lawsuit.
But, in the U.S. Supreme Court case of Daimler AG v. Bauman, 571 U. S. ___ (January 14, 2014), general jurisdiction was limited to the state where the headquarters of the business is located, or another state the defendant is otherwise equally "at home." (For example, the state where Amazon.com chooses to locate its proposed "HQ2" in the case of a lawsuit against Amazon.)
If so, the foreign plaintiff member of the class can probably join the lawsuit, since general jurisdiction is present.
When The Forum State Does Not Have General Jurisdiction Over All Defendants
But, if the forum of the class action lawsuit is not one of the typically one or two states where the defendant is "at home", then a U.S. Supreme Court ruling from June of 2017 that significantly changes the law of "specific jurisdiction" probably bars the joinder of the foreign plaintiff as a member of the class. This case holds that specific jurisdiction over a defendant arising solely from the fact that it sold a defective product in a particular state or country which it caused an injury to be limited to plaintiffs who actually purchased the product or suffered an injury in that state.
So, if there is more than one defendant, the forum state must have general jurisdiction over all of the defendants, or must have specific jurisdiction over all defendants over whom it does not have general jurisdiction for a reason that applies to all members of the class bringing the lawsuit.
For example, if the defective product was an airplane that crashed in California as a result of a defective product, everyone hurt in the crash could sue in a single action in California because that is where the injury occurred to all of them, even if the people on the plane who were injured or died came from different states and countries.
Similarly, if the product was defective as a result of design work conducted by multiple large corporate defendants with different home states outside Colorado that took place entirely at a design collaboration workshop at the University of Colorado at Boulder, a class action including all persons injured globally by the defective products could be brought in Colorado, even if the injuries were dispersed all over the world at places where the defective products were delivered.
The case adopting this radical change in the law of specific personal jurisdiction is Bristol-Myers Squibb Co. v. Superior Court of Cal., San Francisco Cty. (U.S. June 19, 2017) in which the court finds that "specific personal jurisdiction" (as opposed to "general jurisdiction") is lacking with regard to the claims of members of the class of plaintiffs who are not California residents in this case brought in a California state trial court (in an 8-1 decision with Justice Sotomayor dissenting). According to the official syllabus of that case:
A group of plaintiffs, most of whom are not California residents, sued
Bristol-Myers Squibb Company (BMS) in California state court, alleging
that the pharmaceutical company’s drug Plavix had damaged their
health. BMS is incorporated in Delaware and headquartered in New York,
and it maintains substantial operations in both New York and New
Jersey. Although it engages in business activities in California and
sells Plavix there, BMS did not develop, create a marketing strategy
for, manufacture, label, package, or work on the regulatory approval
for Plavix in the State. And the nonresident plaintiffs did not allege
that they obtained Plavix from a California source, that they were
injured by Plavix in California, or that they were treated for their
injuries in California. The California Superior Court denied BMS’s
motion to quash service of summons on the nonresidents’ claims for
lack of personal jurisdiction, concluding that BMS’s extensive
activities in the State gave the California courts general
jurisdiction. Following this Court’s decision in Daimler AG v. Bauman,
571 U. S. ___, the State Court of Appeal found that the California
courts lacked general jurisdiction. But the Court of Appeal went on to
find that the California courts had specific jurisdiction over the
claims brought by the nonresident plaintiffs. Affirming, the State
Supreme Court applied a “sliding scale approach” to specific
jurisdiction, concluding that BMS’s “wide ranging” contacts with the
State were enough to support a finding of specific jurisdiction over
the claims brought by the nonresident plaintiffs. That attenuated
connection was met, the court held, in part because the nonresidents’
claims were similar in many ways to the California residents’ claims
and because BMS engaged in other activities in the State.
The high court finds that the absence of an in-state injury or injury to a resident plaintiff is controlling. It is not sufficient in the high court's analysis that the corporation is already subject to suit in California as a result of its conduct in California to most of the people in the suit. Instead of analyzing whether California has jurisdiction over the product liability situation, in general, the high court decides that the determination regarding whether California has jurisdiction over a suit against a particular defendant must be made on a plaintiff by plaintiff basis when "specific jurisdiction" rather than "general jurisdiction" is involved.
Sotomayor's dissent in this case emphasizes implications of this ruling in the kind of situation posed by this question at Law.SE:
Three years ago, the Court imposed substantial curbs on the exercise
of general jurisdiction in its decision in Daimler AG v. Bauman, 571
U. S. ___ (2014). Today, the Court takes its first step toward a
similar contraction of specific jurisdiction by holding that a
corporation that engages in a nationwide course of conduct cannot be
held accountable in a state court by a group of injured people unless
all of those people were injured in the forum State.
I fear the consequences of the Court’s decision today will be
substantial. The majority’s rule will make it difficult to aggregate
the claims of plaintiffs across the country whose claims may be worth
little alone. It will make it impossible to bring a nationwide mass
action in state court against defendants who are “at home” in
different States. And it will result in piecemeal litigation and the
bifurcation of claims. None of this is necessary. A core concern in
this Court’s personal jurisdiction cases is fairness. And there is
nothing unfair about subjecting a massive corporation to suit in a
State for a nationwide course of conduct that injures both forum
residents and nonresidents alike. . . . It “does not offend
‘traditional notions of fair play and substantial justice,’”
International Shoe, 326 U. S., at 316, to permit plaintiffs to
aggregate claims arising out of a single nationwide course of conduct
in a single suit in a single State where some, but not all, were
injured. But that is exactly what the Court holds today is barred by
the Due Process Clause. This is not a rule the Constitution has
required before. I respectfully dissent.
The most serious issues arise in one of the situations that Justice Sotomayor addresses which the majority does not adequately consider in the rebuttal in its own opinion, which is the situation where there are multiple possible defendants with different home states, whose relative liability is unknown or independent or mutually dependent.
For example, suppose that the product has two kinds of defectively manufactured components manufactured by companies with two different home states in the U.S. (e.g. an electronic device charging bay and a battery) that are assembled by the customer after they are delivered independently, which, when acting together, cause the assembled product to be dangerous and cause injury even though the design itself is not defective. Under Bristol-Myers, there is no U.S. forum with jurisdiction over all injuries caused by these compound manufacturing defects that can allocate responsibility between the responsible manufacturers on a consistent basis.
Why Didn't It Matter That The Drugs Were Distributed By A California Distributor?
The high court is also unimpressed with the fact that the drug giving rise to the product liability was distributed by a California company, presumably because the cause of action in question in the case was brought against the manufacturer as a strict liability defective product claim, rather than as a claim against a seller of the product arising from a warranty that the product was free of defects arising under the Uniform Commercial Code or an express warranty.
This makes sense if the California distributor was a wholesale company not in direct privity with the retail buyers of the products from retail pharmacies who were injured by the products. The wholesaler could be sued under the Uniform Commercial Code on its warranty to the buyers of the drugs, only by the intermediate wholesalers or retail pharmacies that bought the drugs. The wholesaler could also be sued on its warranty only if those direct buyers themselves suffered injuries as a result of the defective product. For example, a retailer might have injuries in the nature of breach of warranty liability in suits brought against retail sellers by injured consumers under the Uniform Commercial Code that the retail sellers would be seeking indemnification of from the California based wholesale distributor.
But, Bristol-Meyers does mean that it is basically impossible for injured consumers who were not injured in the forum state to sue both the manufacturer of the defective drugs (where jurisdiction would be present in New York and New Jersey) on a tort theory, and the distributor of the defective drugs (where jurisdiction would be present in California) in the same action. So, it is effectively impossible in this case for all people injured by the defective drugs to sue all of the potential Bristol-Meyers case defendants in a single lawsuit.
Statutory Considerations
Existing statutory limits on federal court jurisdiction limit the jurisdiction of the U.S. District Courts in most cases of cases to cases in which a state court in the state where the U.S. District Court is located would have either general jurisdiction or specific jurisdiction of the defendant (without regard to the fact that the case might be within the exclusive jurisdiction of the federal courts as a matter of subject matter jurisdiction which pertains to the nature of the cause of action asserted rather than the ties of the defendant to the forum state).
But, the decision leaves Congress with the option of potentially changing that statute which currently limits the personal jurisdiction of federal trial courts to that of a state court of general jurisdiction in the same state, as it already does in cases that are predominantly "in rem" (e.g. interpleader cases and interstate boundary and real property title disputes), in bankruptcy cases, and with respect to the subpoena power of U.S. District Courts.
The official syllabus also notes that:
The Court’s decision will not result in the parade of horribles that
respondents conjure up. It does not prevent the California and
out-of-state plaintiffs from joining together in a consolidated action
in the States that have general jurisdiction over BMS. Alternatively,
the nonresident plaintiffs could probably sue together in their
respective home States. In addition, since this decision concerns the
due process limits on the exercise of specific jurisdiction by a
State, the question remains open whether the Fifth Amendment imposes
the same restrictions on the exercise of personal jurisdiction by a
federal court.
Constitutionally, Congress still has the authority to vest all U.S. District Courts with jurisdiction over any case in which the United States treated as a single state for purposes of general jurisdiction and specific jurisdiction analysis. This would leave the question of which particular U.S. District Court was the proper one to file in as a question of venue (which does not have a constitutional dimension) rather than a question of jurisdiction (which is subject to constitutional considerations), and many legal scholars have urged Congress to do just that. But, so far, Congress has not altered a status quo that does not give U.S. District Courts the maximal jurisdiction allowed under the United States Constitution.
But, so far, Congress has instead taken an intermediate position on the geographic scope of federal court jurisdiction in the jurisdictional portion of the Class Action Fairness Act of 2005 (which also limits the extent to which "coupon settlements" of class action cases are permitted). In particular (per the link in this paragraph):
The Act permits federal courts to preside over certain class actions
in diversity jurisdiction where the aggregate amount in controversy
exceeds $5 million; where the class comprises at least 100 plaintiffs;
and where there is at least "minimal diversity" between the parties
(i.e., at least one plaintiff class member is diverse from at least
one defendant). The court, however, may decline jurisdiction under
certain circumstances, and is required to decline jurisdiction in
certain others.
But, while the Class Action Fairness Act of 2005 allows many class action lawsuits which would otherwise be brought on exclusively state law claims in state court to be brought in federal court, or removed from state court to federal court, it does not authorize class action lawsuits that could not be brought in a state court which a U.S. District Court is located due to lack of either general jurisdiction or specific jurisdiction from being brought in that federal court either.
The Class Action Fairness Act of 2005 was favored by businesses likely to be defendants in future class action lawsuits (such as manufacturers), because state civil procedure law in some U.S. states such as California, is more favorable to class action plaintiffs than federal civil procedure laws related to class actions.