I don't believe the school will care that you are now qualified for FAP. If anything, it signals that you have no offers which could create an unconscious bias on the part of the people who receive this news.
Agree with @LizzyM : FAP helps you as an applicant, and it's on you to know if you are eligible and can take advantage. Schools don't get any of the money you have been granted from an FAP, and schools don't get an award from AAMC for admitting the most FAP recipients.