If that other republican had gone all apologetic then for sure he would have lost. But if they'd done what Trump did and just shrugged it off it then no. Republicans don't care if their presidential candidates assaults women, hires prostitutes, is a racist, or do any of the other disreputable things Trump has done. They just don't want someone to be weak about it. That's what Trump recognized. As long as you don't apologize for being a racist. As long as you don't apologize for sexually assaulting women republican voters don't care. Just ballzy through it and you'll get their vote.