I've had a couple of Doctors who stammer. They were just as competent as the others, but I felt more comfortable around them because they had a "flaw" like me. They weren't perfect humans I put on a pedestal in my head. They seemed more human. Since your son isn't shy about his stammer, he should lead with it. Let people know right away that he stammers (especially right before presentations). Medical schools care if you know your practice and whether you're empathetic enough to help cure people. I doubt they'll care about his stuttering. Best of luck with medical school!