Here's my take as a BGO and USNA roommate of someone who did the med school thing.
Z is right. The purpose of USNA is to prodiuce line officers, not physicians. That said KP is right in that a certain number of mids each year are permitted to attend med school directly from USNA.
What you should know:
(1) This program exists at the pleasure of the USN, meaning they can discontinue it at any time. They did this in the late 1970s. Prob won't happen, but if it does, nothing you can do about it.
(2) The USN decides on the number of mids who can attend med school and the school you will attend (based on where you are accepted, of course). I've been told that two years ago, about 24 mids went to med school and last year the number was about 12. Not sure whether there was less interest or a drawdown. Still, the number of mids who can attend med school is based on the needs of the Navy. Thus, being accepted is not a guarantee that you'll get to go.
(3) Telling your BGO and/or CGO that your main desire in life is to attend med school right after USNA is not going to help you. If that truly is your desire, as Z said, you probably should go NROTC. BTW, I am NOT suggesting that you lie about your intentions. Just saying that if your intention is to be an MD first, maybe USNA shouldn't be your first choice for college.
(4) When I went to BGO training several years ago, the then-head of medicine at USNA (a grad, BTW), said that if you want to be a doctor, do something else first. His view was that you only have one shot to drive ships, fly planes, lead infantry. You can always be a doctor. He recommended strongly advising candidates who want to be an MD and want to attend USNA to go into the line for a few years and, then, if they still want to be an MD, go for it. Just his opinion, of course.