I'd say No. He and his advisors might have wanted to, but I doubt that the public would have supported him if they weren't scared like crazy (as many were in RL after 9/11). Back in 1990-1991, nearly half of Americans opposed entering the Gulf War (even though the U.S. was just liberating one of its allies, not invading another country). Thus, I doubt that many people would have supported American entry into Iraq without 9/11 or a similar terrorist attack. The U.S. economy was in poor shape between 2001-2003, so if people were not scared, they would have criticized Bush for invading another country instead of worrying about domestic problems and the economy.
A justification would have been found/created.
Basically, this.
When a militarist wants to lead his country to war, an excuse is created. Remember, Germany only invaded Poland because the Poles first attacked Germany...