Pence may have a brain, but hasn't used it for so long that it probably isn't functional. If he did, he would jump at the chance to be POTUS even for a few minutes. But his lips work and he has been kissing trumpers ass for so long that he cannot let go.
So, no. I don't think anything will happen. Trump.will.be impeached and the trial will happen after he leaves office. So pence never gets to be POTUS.