Well… is that the POD?
Because it seems to me Clinton is not the sort of person who would vote against the war. It seems to me that she both believed in going to war, and did so out of political positioning for her Presidential run.
For her to vote against the war would require her to be quite a different person, or for the Democrats of that time period having something resembling a spine so that she could go along with them.
Even assuming she did vote against the war it really doesn't help her as much as you might seem to think. "Progressives" still don't like her, she's still running with the same poor campaign team, and so on.
Does it increase her chances of winning? Absolutely. But it's not some foregone conclusion the way you present it.