The General Rule
Even if the charge is presented to a grand jury and it declines to indict, exactly the same charge that one grand jury declined to indict upon can be presented to a future grand jury and produce a valid indictment.
A charge upon which a grand jury declines to indict is often not presented to a future grand jury as a matter of prosecutorial discretion or prosecutor's office policy, but generally this is not a mandatory rule.
There may be some jurisdiction in the U.S. where this is not the case, and such a statute would not be unconstitutional if it were, but I am not aware of any state where this is prohibited, and I do not believe that this is the case in federal court.
Justifications For The General Rule
One reason that it is not a mandatory rule is that there is no practical way that a defendant could enforce the rule if it was a mandatory rule. Grand jury proceedings are secret (at least until an indictment is produced and then only as pertinent to the defendant indicted on the charges producing an indictment).
Generally, even the judges in the court calling a grand jury have no access to its proceedings until it issues an indictment, and then has only slightly more latitude to review its proceedings than a defendant in the case.
Agreements To Dismiss A Case Distinguished
A prosecutor with jurisdiction over a criminal case that is presented to a grand jury could reach an agreement with a defendant that is binding not to prosecute on a charge in the future, but again, that would be an affirmative act of a prosecutor agreeing to honor a grand jury "no bill" and there would be no legal requirement that the prosecutor do so.
Note, however, that there is a downside to repeatedly bringing a case to a grand jury after receiving one or more "no bills". A prosecutor has a constitutional obligation arising under the Brady v. Maryland, 373 U.S. 83 (1963), to disclose all exculpatory evidence known to the prosecutor to the defense, upon request.
Usually, when a grand jury declines to indict there is something in the evidence presented to it that is exculpatory. A repeated presentation of charges that one or more prior grand jury rejected that ultimately produces a grand jury indictment would usually be strongly suggestive of the fact that there is exculpatory evidence in existence that may not have been disclosed to the final grand jury and that needs to be disclosed to the defense prior to trial.
Also, many criminal charges have a statute of limitations, and charges cannot be presented to a grand jury after the statute of limitations for the offense has expired.