Kill alternator by charging a dead battery?

can jump starting a car with a bad alternator damage the alternator in my car ?

Well, I had my alternator on my 96 Dodge rebuilt this summer because it was noisy. The van had 125K miles on it and the alternator was still charging, and I know that over the years I charged a few run-down batteries. Now it might have gone longer if I had never done that. But I was satisfied with the performance of the alternator.
I might add: I have had pretty good service out of the old Dodge.