Perhaps, i doubt it. They usually only pull a license for a felony or a medical mistake. I seriously doubt this goes to a felony.
If he is dismissed, that is equivalent to a bad conduct discharge, and his separation papers will show "other than honorable". That's enough in many states to get your professional license pulled, or never issued as the case may be. In others it's the conviction itself, not the punitative discharge/dismissal.
He might have to go practice on some Caribbean Island, like Grenada. Maybe he could teach at the True Blue campus of the St. George's School of Medicine? ;). He's not been in the Army long enough, unless he had a break in service, to have served there back during Urgent Fury under a Real CIC, R. Reagan.
BTW, in looking up the effect of a punitive discharge, I discovered that anyone sentenced to one gets an automatic appeal to the Court of Military Review for their service.