I find it implausible that any politician who is a product of the party machine - which Trump is decidedly not - has skeletons in their closet that haven't been well researched, studied, catalogued, and filed by both their own party and by their opposition and would have been removed from any shortlists for candidacy at the VP stage, let alone the presidential ticket.
This is assuming there's people with the will and focus to conduct thorough background checks on such persons, and for such persons to be 100% truthful to the party. I'm doubtful either are ever completely true, and shit will definitely slip through the cracks.
People like to think The Party or The Illuminati or whatever have their hands on the wheel at all times, safely guiding Earth's destiny even if it's to ends we don't like. The truth is no one has their hand on the wheel, there are no guard rails, and we're cruising 100 MPH towards a cliff a few miles down the road.