I haven't checked the language itself but it's my understanding that a president cannot serve more than two terms, so if s/he were vice president when the president died or was removed from office, s/he could not be elevated to president.

On the other hand, what about when a vice president finishes out a president's term- s/he is still legally able to subsequently serve out two full terms of his or her own. Guess I'd better check out the language.