Not for long.
Drama from Rudy's personal life isn't going to hurt him.
What can sink him, if Rudy isn't aggressive, is this. People like Rahm Emmanuel and Chris Lahane will probably try to take Giuliani's greatest advantage, 911, and turn it against him. People will support a scoundrel these days, but they are skeptical of heros.
If Giuliani is aggressive and goes out with a kick-ass attitude, that won't be a problem. If he looks like an incompetent, flatfooted politician like Bill Frist during the primary fight, well, he'll lose-- it would sound like Kerry droning on about how he served in Vietnam. Hopefully the Giuliani from the national convention shows up, and not the Giuliani who lost a 140-page document last week.
Trial by fire during the primary season is the only way to know. And unlike FR, most Republicans in 3D space want someone who can win.