I'd say there's a pretty good chance of exactly that happening. This particular Kurdish group is considered terrorist, even by the US, but the nations of that area have never taken kindly to the establishment of a Kurdish nation, even one outside their borders. Iran has already shelled parts of Iraq in retaliation to cross-border raids by this particular group.

The Kurds have the most successful "state" in the area, and are in no mood to rat out on their pals, terrorists or not. And everyone there feels we are pro-Kurd and resent our protection of them. At the very least, the US will be embarassed by military action into Iraqi Kurdistan by one of our allies, particularly one that plays an immense logistic role in our war plans, and everyone else in the region is trying to figure out how to take advantage of this situation and prevent their neighbors from profiting from it.

It's what a friend of mine once called "a very touchy shituation".