Hadn't heard Aaronoff was in it, but Alphonse Mouzon was the jazz trio drummer and had a decent solo cameo. Tom Hanks actually wrote some of the music used in the film, which in my opinion was really well done and period correct. Not too many movies I can think of where the drummer was actually considered the brains of the outfit either!
I did some research and he wasn't in the movie but he did record the drums for The Wonders "That Thing You Do" single from the movie and maybe the other songs too