Would Hillary Clinton be President if she voted against the Iraq War resolution?: Maybe.
It's easy to see issues as the driving force behind Presidential elections. In that case, the Iraq War issue can be seen as a decisive advantage for Barack Obama in 2008. But that's much too simplistic. I subscribe to the line of thought that presidents are elected because they set up well organized campaigns. The Clinton campaign's "Hillarycentric" leadership style along with over-centralization in Mark Penn bear far more responsibility for her defeat than her vote on Iraq. Had Clinton run a better campaign than she would have won, Iraq or not. The Obama campaign outplayed her, and she shot herself in the foot. The War in Iraq was merely Obama's "foot in the door." It gave him a wedge issue to use against Clinton. But it did not win him the Democratic Nomination.
P.S.: I believe very firmly that Clinton could have embraced her vote in Iraq and still won the nomination. Had her campaign invested in a ground game in Iowa, targeted young voters, emphasize her life story, and portray her as a strong and effective leader, than she could have easily won the nomination. The Iraq War could have been used as part of a narrative focused on strength and determined leadership. By waffling on the issue, Clinton legitimized Obama's opposition to the war and gave him a "win."