More likely, an attempt will be made to turn Iraq into a client or satellite state, the way Syria had Lebanon under its thumb for many years, and clearly wishes to do again.
I expect the Al Qaeda will get slaughtered once we leave, and I doubt that Syria or Iran wants to grab the Iraq tar baby. And at any rate, eventually things will likely settle down to some sort of order, which will never happen while we are there.
Do you have any reason to believe that we can ? Just by being there we make that nearly impossible; for one thing, any Iraqi government that takes power under us is tainted and illegitimate. Not to mention dead or fled when we leave.
We are the bull in this china shop. The solution isn’t to try to tame the bull while it’s in the shop or, even worse, add another bull in hopes that it will stabilize the first bull. The solution is to drag that bull out of the china shop as fast as you possibly can, pay for the damage your bull has caused, and let the shop owner decide how, if it is even still possible, she wants to repair what your crude manners have done.