So your application can actually be "approved" prior to an acceptance letter from an MD/DO school, it just cannot be sent out for final review approval until you have an acceptance in hand.
There are technically 2 stages to the review process: 1) a professional board recommendation and 2) a review board recommendation. The former determines whether your application is suitable (read: likely to be accepted to a school) and then, upon acceptance to a medical school, your file is moved on to the review board for final approval.
At least this is how my recruiter explained it to me (Navy). Also, it need not be from where you will finally attend school (assuming multiple acceptances). The actual school you chose to provide with your application does weigh into how your application is viewed, however. Example being, Applicant A applies to Q'pac/30MCAT/3.5 GPA and Applicant B applies to UNC/30MCAT/3.5 GPA the latter candidate has a much better shot at being funded (again, Navy side) as they want physicians from more well established schools if possible, and they have limited slots to award each year.
That said, I've only heard of a handful of people who volunteered for the HPSP who did not receive it for reasons other than medical disqualification.
Hope this helps!
EDIT: spelling