Yes, it’s background the same way as the FBI would put in a government security clearance file anything about your past. If it’s a questionable state law issue, they will note it down and you might end up getting denied a clearance or having your appointment or nomination withdrawn, but they normally wouldn’t launch a full-blown investigation of something that didn’t involve a federal law, unless maybe the President told them to, which this President is unlikely to do.
Nowadays the federal law is so far-reaching that almost anything might be tied to a federal law violation, but I think misbehavior at a high school party is one of the few things that doesn’t quite make it.