Only if the tension wasn't right on the belt. If that was the case, I could see the engine flopping around internally.

I charge $300 to do a timing belt job, with all the goodies. So if the $350 includes his diagnosis and he'll guarantee the fix, then it's a good deal. If not, then he's there already, just put the teeth right and verify it. If it's not right, he can re-diagnose it for the money you've already paid.