This is actually a somewhat interesting historical "what if?"
Politics (mostly) aside, I think that WMD and 9/11 both have to be considered when contemplating this question.
Consider: Iraq was a "thorn in the side" that even the previous admin could not completely ignore. Moreover, though it was rather low-intensity, as others here have pointed it, it was still very much a shooting war.
Consider: Prior to 9/11 the actions and activities of the current President made clear that there was an intense interest in international terrorism, Al Queda, and Iraq.
Consider: The general gist of the current administration seems to be active/proactive.
Consider: W/out the WMD "issues" (which predate the Kuwait invasion) it seems probable that Iraq itself would have been different in 2003 - indeed, an invasion by a neighbor, or a successful internal revolt seem very likely if there was no fear of WMD.
My read is that w/out 9/11 -and perhaps an Iraq that was considered to be a lesser threat WMD-wise, though still threatening enough that Iran had not invaded, or whatever - the current CIC would have pushed things in that region quite a bit. Perhaps not a direct invasion, but more than some flyovers and a couple of TLAMs.
With 9/11 we have the courageous decision to build the "Bush Doctrine". While generally considered as "pre-emptive conflict", in point of fact Iraq already was a conflict, and moreover the Doctrine itself appears to be focused more on recognizing that when faced with state/sponsored or harbored international terrorism the US is in fact in conflict. So, while the Doctrine is not correctly pre-emptive (e.g., let's nuke China before they get too big for their britches), it appears as though it does not require a specific threat such as WMD.
If we continue with the hypotheticals, it seems very clear that on the Iraq side activity was actually increasing in boldness, including moves to remove sanctions, etc. Remember: Iraq was a very public sponsor of international terrorism. If the US had responded to 9/11 etc. with weakness, it seems probable that Iraq would have increased this sponsorship, and increased sponsorship of terror attacks against the West in an increasingly public fashion.
So, what we really have in the WMD "issue" is a fairly predictable amount of battlefield noise in a conflict that was ramping up in intensity. "Fog of war", if you prefer. The conflict was there, and it was not going away. While it may not be 100% certain that an invasion was inevitable, some form of regime change was very probably on the table.