If you thin joining the military is going to accelerate your admission to medical school, you are mistaken. It will easily add 4-8 years to the endeavor (it's a service contract, after all), and you won't have as much free time to devote going to a classroom for a DIY post-bac. Your operational responsibilities will trump any deadlines/deliverables. Got a mandatory lab? Too bad, you're on the watchbill and you have to stay on base. 20-page paper due? Too bad, you're going on a week-long field exercise without access to a computer. You want to register for classes for next semester? Too bad, we're deploying overseas. All these things happened to me while earning my Master's while on active duty.
It will, however, give you amazing ECs, leadership opportunities, and ways to broaden exposure to the field of medicine and the world. Just make sure you join the right team... like my beloved Hospital Corps.