I don't think so. We had a Shih Tzu with an underbite, and he was fine. He died a few years back from old age, but it was nothing to do with his teeth.
Shih Tzus are awesome, btw. They are the perfect breed, in my opinion! My family (parents, brothers, sisters, myself, etc) has had 13 of them so far, amongst all of us.
Cutest. Dog. Ever!