Yes, B -> E sounds good, even if you're in the key of A major.

As you suggest, it's the power of the V -> I progression. If you have any doubts, play it as B7 -> E, and see if your ears hear it as functionally the same. If so, it's a V -> I progression in action.

Depending on context, you'll probably just hear it as a temporary modulation.

-- David Cuny
My virtual singer development blog

Vocal control, you say. Never heard of it. Is that some kind of ProTools thing?