Would a U.S court honor his request, based on his prior commitment?
You are not specifying the purpose of the court hearing, or whether Adam is pro se litigant (which sounds unlikely if this plaintiff is a movie star).
If plaintiff Adam is represented by an attorney, Adam's presence is unnecessary in most or all court hearings. In fact, typically neither parties nor their lawyers have to show up in court, whence their absence does not constitute contempt of court. Absence merely implies that they miss the opportunity to [orally] argue their position before the court, and thus would depend on whether the judge bothers to actually read their brief.
If you mean a hearing in which Adam needs to be present, his request to reschedule the hearing is most likely to be granted. His contract is strong evidence that his request is not a vexatious attempt to delay proceedings. Since the hearing would be in month 4, the particularity that his contract goes up to month 4 implies that rescheduling would not significantly delay proceedings.
Regarding your comment, rescheduling can (and does) happen multiple times even in criminal cases. This post includes an excerpt of the Register of Actions of criminal case 16-870-FH in Michigan state court (Washtenaw county), highlighting several instances of rescheduling as requested by the defense counsel and despite prosecutor's objection. I believe the case got rescheduled a few more times beyond what the snapshots reflect.