Yes and no. It does make it less likely that Giuliani would be Trump's running mate, but I know they are fairly close. Neither the constitution or the electoral college prevent a presidential candidate from choosing a VP from the same state. But in the case of a close election it could complicate matters in the electoral college. So as far as I know it has never been done, but it actually is possible and not against the law.
I will swim against the tide a bit - it won’t be Sarah, but I would not be surprised if it was a female. From a purely political standpoint it softens his image and removes the stupid female card from the equation.
However, I would not mind Gingrich getting the nod. He knows how to get things done in Congress and he was without a doubt the most effect GOP Congress critter of his generation.