From my understanding, yes she would be sworn in and function until the next candidate was elected.

As she is the current VP candidate, I believe she would just get bumped up to the presidential candidate and they'd need to decide a new VP.

Now what I am not quite sure of is what would happen if he died mid-election after people have already voted for him. Would they do another run of ballots? It ultimately wouldn't matter much, but I would be curious what the mechanics would be.