Not for Trump it wouldn't.
Trump needs a respected Senator with DC connections and some foreign policy experience if he's going to play 'let's fill in the gaps.' Kasich will win him Ohio and brings strength to the budget issues but.......(ftr - since the end of the Cold War, foreign policy doesn't even show up on the radar sans 2004)
Bill.....the problem I see with going with a Senator is that it conflicts with his campaign platform of being an outsider.
A governor OTOH still maintains Trump's outsider appeal......but will bring with him/her the experience of running a government......without the baggage someone from Washington will most certainly have.
Now if you are of the opinion he needs a Ying to his Yang.....then your premise would be a valid one. I think the outsider movement is his key to victory.