yes, you will have free time. in garrison life it's generally for the most part like any normal day job. you go to work, you go eat lunch, you go back to work, then you go home for the day.
if you are good at mma it's possible you could become the company/battallion/brigade combatives nco.
i am pretty sure the lowest enlistment contract is like 6-8 years.
if you are serious about your fight training, maybe check out the reserves or national guard? you'd get same training as your active counterparts, and minus one weekend a month and a two week block of summer training, you'd be free to continue to train/fight.
fwiw, the army is the bomb. seriously. best life decision i have made to date. even better than deciding to lift weights.