At our school, the Admissions Committee reviews all felonies. Nothing would exclude them from attending school, but we have contacted the Board to see if something would disqualify someone from getting a license. If so, we feel it would be unfair to accept them if they would be unable to be licensed. I think we have had 1 applicant in my 5 years on the Admissions Committee (and we get well over 1,000 applicants/year), so contact the school you are applying to and ask them.
At my school we also review all felonies, and also contact the state board to see if it would affect their ability to be licensed. If your friend does have a felony conviction, they should not try to hide it. Schools may not immediately require a background check, but many clinical sites do. It your friend does not disclose it and it comes to light later, it may not end well for him/her.
I agree with what others have said. Best to be honest upfront. Also, at my school, I remember some students having to get noise violation citations expunged before being able to go out on their first clinical rotation. One girl was rather upset because she had attended undergrad out of state and had to go to that state to get it taken care of.