This is the crux of the issue; your assertion can be judged as being directly contradicted by Lieberman's victory in CT. There is a big difference in protesting against the war in order to score political points vs really wanting the US to lose.
The Rudy calculus is simple: are there more than enough centrist Dems who, even though they oppose the war, would really vote for defeat vs the number of SoCons who will not vote for a social liberal?
I think it's going to depend much more on who the Dems are likely to nominate.
Rudy matches up well against Hillary! due to the fear factor which might induce some SoCons to still vote for Rudy. However, I do not believe Gore engenders the same level of visceral dislike, which might be a problem in a tight race. Under that scenario, I think Gore takes in 2008 if he is nominated by the Dems.
Lieberman was elected because the Dems in CT woke up to the fact that the DU/MoveOn types were trying to foist a whacko on them. That, combined with an effort to get Reps to cross the line promoted on this very site(!) is what elected Joe.
Since then, national support for the WoT has slipped, and Hill has been tailoring her stance to match the polling data.
Under that scenario, I think Gore takes in 2008 if he is nominated by the Dems.
Gore isn't running, unless I've missed some major news. Gore is consolidating his "green" position, so as to act as kingmaker, now that the McAuliff Machine has imploded and the Deaniacs never gelled.