One well-known chap in Melbourne (certainly would have to be retired now - haven't spoken with him for quite a few years) ..
(a) started off as an airline F/O (ANA - long time ago, now),
(b) read medicine while flying, eventually discontinued airline flying and ran FT with medicine - but could have combined the two without too much difficulty,
(c) subsequently read electrical engineering and ran a successful avionics shop
all the while having an interesting life of it. Not the common path due to the training time, but feasible, nonetheless.
I think you may have misunderstood, but my apologies if you haven't. But as far as I'm aware, there is no medical degree program, and by that I mean, that awards one with a MBBS, that is offered part-time. Sure, you can read every book in the world related to medicine, but it doesn't admit the individual for an internship which is what all medical practictioners must complete.
I stand to be corrected, but I myself only graduated from year twelve last year with an offer to UNSW's MBBS program. Unless anything significant has changed since then, I don't think medicine would be a good choice if flying is what one wanted to do full-time IMHO. However, full-time medicine and recreational flying is certainly feasible and probably the more sensible out of the pair.