I think we need some clarification about “Ivy-ish.” Academically, I know what you mean by Ivy-ish. However, for athletic recruiting, there are exactly 8 Ivy League schools.
The Ivy League has some very specific rules about coach support so an athlete is really either on the finite list for coach’s support or they are not. This process is very proscribed league-wide, so there is no room for a coach to negotiate to go in halfsies with a music program on an admit. In the Ivy league, recruiting is all about the slots, with a small number of athletes getting in on their own.
For most other D1 programs recruiting is about scholarships (and now NIL-type) money and roster slots (especially for minor mens sports). Admission “help” that is available might vary from school to school and sport to sport, but it’s not driven (too hard) by league rules. A D1 swim coach I was speaking with recently told me he has and wants no pull with admissions. I am sure the basketball coach has a different story, though. Being recruited at Stanford will require strong academics, but that’s separate from what the ACC requires.
If I were a coach, my concern would be about scheduling conflicts. Are rehearsals the same time as workouts? Is the conference tournament the same weekend as the fall concert? These concerns might be show stoppers or nothing-burgers.