Nothing will stop you from reading or writing if you have the time. Plenty of doctors write well and often, and I assume that that statement applies to their reading as well. Atul Gawande, for example, is a fantastic writer who frequently wrote pieces for the New Yorker (and other publications), on top of writing full-length texts.
What is your primary interest? If you dont want to practice medicine at all - if you want to focus on your literary interests - then you should probably spare yourself the agony of pursuing an MD.
Do you just want to be a practicing physician who still flexes his literary muscles? Maybe you should try one of the ROADs specialties, so you can practice and have "me time," to devote to these interests. That said, Dr. Gawande (who I mentioned above) is actually a general surgeon, and they aren't know for having hours to burn. (Disclaimer: I don't know whether he was otherwise employed while he wrote. It's quite possible, as surgeons are said to just work work work sleep work eat and work.)
What I'm trying to say is, you have options. If you don't plan on practicing medicine, maybe you shouldn't bother with an MD. If you want to be a practicing doctor, you'll be busy a lot of the time, but can pursue literary endeavors when you're off duty, as other physicians before you have done.
