"Extensive" is a bit of a stretch. You get about 10 hrs of flight time at AMP (AF Flight Surgeon "school"). The certain amount of flight hrs every month (at least in the AF) is 4, which can range from multiple 0.8 sorties in something fast and fun to knocking them all out in one flight taking a nap on a heavy. All depends on your assignment which is by and large a crapshoot.
A buddy of mine is a Navy FS and they actually do significantly more flying, up to (and maybe including, but I never heard if he actually did) soloing a T-6.
So if you want to learn a lot about flying from the military, you'd get more of that from the Navy.
To the "flight surgeons are not pilots" above (sorry I didn't quote it...): this is true. The AF is, however, very actively recruiting into the 48VX career field which is Pilot Physician, which may be something you want to look at if you are young enough and OK with doing something less clinical than a typical medical career. This incurs a $h*t-ton of ADSC and from what I've seen, you better be ready to be a career guy.
This is the most common route though often, and in my case, unintended. Experiences during FS tours are very widely variable. I got lucky with mine. Like you, I intend on entering a surgical specialty after my time here. All this being said, if you get offered a categorical training spot straight of of school, TAKE IT. The mental/clinical atrophy as a FS is very real.
Hope all this rambling helps with your decision. I'll be spending the next ~4.0 hrs in a 130.