My small org researched this question for someone last year. Here is the info in synopsis.
First, I was unable to determine if the med schools themselves do a credit check as part of the application process.
As for the money, Staffords have no credit check. But most folk will need beyond them to make it through, and these do indeed have a credit check.
Essentially, if you do the BR, you must seek to establish new credit ASAP, and be utterly perfect with it for about three years before they venture the risk.
But this is only what was found by approaching one particular lender at random. Others may have more stringent or less stringent requirements.
I'd suggest you NOT call the U of Tenn SOM and give them your possible scenario, "Hi, my name is so-and-so. I was wantin' to ask you, if I do a BR, can I still get aid?"
Instead, simply call them for the info on lenders they use, or better yet, call the lenders you already use. Give them and them only the whole possible scenario.
But do protect your privacy, be as anoymous as possible, as you investigate this all.
Winning a NHSC scholarship would sidestep all this and make it irrelevant, unless of course they do a credit check as part of their evaluation of candidates.
Even so, I understand from a BR lawyer that it is illegal for people and entities to discriminate against you in such things. Whether they do or not is of course another matter.
Best wishes.