I wasn't even allowed at my graduation for various reasons, but I am absolutely certain they played Good Riddance. This is an empirical certainty. There is no possible way they didn't play Good Riddance. The worst part was, most people at my school had OK taste in music, but they chose Good Riddance because that was just the song you played at Graduation.
I am actually pretty glad I wasn't allowed to go, because they didn't register people who skipped out on it without a good reason as having graduated, so I still got a diploma, and I didn't have to sit through that goddamned song, and I didn't have to wind up in hospital or anything.
Personally, if it had been upto me, I would have chosen "A Hard Earned Thirst Needs a Big Cold Beer, But I Drink To Get Pissed" by TISM, because that song pretty much describes Graduation night, and it would look awesome played over shots of kids running out from the school hall, and shots from the chaotic parties that ensued, if we were in a Teen movie or something.