They will indeed. The vast majority of Iraqis have no desire to wind up with a theocratic goverment like Iran. So long as Iraq remains a republic, it won't. As in the rest of the world, the extremists are a small, small percentage of the population. Sunnis may be willing to sit back and let the wack jobs do their dirty work for them, as far as fighting the foriegn invaders, but they have no intention of letting them actually run the government.
There is a certain nationalistic / Arab pride that many Sunnis feel when they see us attacked. That's why a blind eye is turned towards them. Once we're out of the picture, the dynamic changes entirely. If we were conqured by the Soviets, and you saw gang members fighting them in the streets, you'd feel the same way. Still, once the Soviets pulled out, you wouldn't vote in a Crip or Blood as mayor. Same principal involved here, as well.
I think I agree, but I haven't spoken with a vast majority with Iraqis so it would be presumption on my part of cast that point in stone.
However, keep in mind, Sharia will still be the highest authority (as spelled out in the Constitution) so there is no constitutional safeguard against an Iraqi-style theocracy. There is nothing to prevent hardline islamists such as Muqtada al Sadr from assuming a powerful role in the government and then pushing for the passing of laws which were the hallmark of the Taliban rule in Afghanistan (all they have to do is conform to Sharia).
My point ultimately is this. We (the west) have somehow come to the conclusion that democracy is the true antidote to Islam (and it might be)...but there is still a big IF. It sounds reasonable for western idealists who love democracy and freedom (I am one) to believe democracy will overpower islam, but there is no precedent.
If democracy fails to take hold in Iraq, we will have to go to plan B in the war against fundamental islam.