No. The circumstances of Kamala Harris's birth fall squarely within the terms of United States v. Wong Kim Ark. As described in the other answer, the fact that Wong's parents had a permanent domicile in the US was not a deciding fact in the analysis.
Some people think that a foreign student, a temporary worker, or an illegal immigrant is just as much outside the jurisdiction of the US as an ambassador, but this is not the case. An ambassador to the United States is literally immune from the jurisdiction of the United States, to the point of being able to escape prosecution for crimes as serious as murder. The same is not true of other foreigners, whether they be lawful permanent residents, temporary nonimmigrants, or illegal immigrants.
In fact, this issue arose with respect to illegal aliens in Plyler v. Doe, as described in a very thorough answer to the question What is the meaning of “and subject to the jurisdiction thereof” in the 14th amendment? on this site. There, Texas argued that children of illegal immigrants were outside of its jurisdiction and therefore not entitled to 14th amendment protections. The Supreme Court found that "no plausible distinction with respect to Fourteenth Amendment 'jurisdiction' can be drawn between resident immigrants whose entry into the United States was lawful, and resident immigrants whose entry was unlawful." Even the dissent found that "the Equal Protection Clause of the Fourteenth Amendment applies to immigrants who, after their illegal entry into this country, are indeed physically 'within the jurisdiction' of a state."
Indeed, as the Cato Institute's Josh Blackman says in Birthright Citizenship Is a Constitutional Mandate, "the reason such people are called “illegal aliens” is that they are subject to U.S. law[s], and not in compliance with them." (I owe thanks to Just a guy for posting the link in comments.)
If illegal immigrants are within the jurisdiction of the United States, then legal nonimmigrants surely are as well, for all the same reasons and, on top of those, because they subjected themselves to its jurisdiction when they applied for a visa (if they did) and when they applied for admission as nonimmigrants under US immigration law.
In response to your edit:
I'd like to emphasize that this question is not about how the Citizenship Clause should be interpreted (...), but whether SCOTUS can be expected to opine on it, in light of recent controversies.
For the question to make it to the Supreme Court, someone would have to assert that someone born in the US is not a US citizen, and someone else would have to challenge that assertion. Furthermore, there would have to be some meaningful consequence of the dispute.
The most likely way for this to happen, it seems to me, is for a federal administration to adopt the position that a person born on US soil to illegal immigrant parents is not a US citizen. At some point in this person's life, it would become necessary to challenge that in court, either to defend against deportation or to seek some benefit, such as a US passport, provided by the federal government. The present administration made some noise a couple of years ago threatening to adopt such a policy, but they backed down, for reasons I cannot discern.
Whether a future administration might go through with it requires a crystal ball to predict, but given the huge headache this would cause every US citizen, who would be forced to document their parents' immigration status at the time they were born, and possibly their grandparents' immigration status at the time their parents were born, and perhaps going back even farther, it seems very unlikely to me.