Not sure - I think that the "war on terror" foreign and military policy inspired to a large degree by the events of 9/11 was needed to justify to the UN and US and global public opinion the invasion of Iraq in 2003. Without that figleaf of justification, it is difficult to see the UN sanctioning what was effectively military intercession to effect regime change.
There was plenty of backstory though, dating back to Bush Sr in the early 1990s, and it is difficult not to see the whole sequence of events as a means of accessing iraq oil and installing a regime more willing to co-operate with the West. On balance, I think that, without 9/11, Bush Jrs desire to finish what his dad started and the US hawkish foreign policy would have been insufficient on their own to gain any sort of support for military intervention, and the 2003 invasion probably would not have happened.