Well Turkey wouldn't invade Iraq with an American presence still there, they know that that would be suicide and most likely get them thrown out of NATO. What is most likely is that if the US leaves and Kurdistan tries to become independent we could see a Turkish intervention in the North to "protect the Turkomen minority from Kurdish oppression" but really to stop the possibility of the creation of a Kurdish state in order to keep these ideas from spreading to Turkey.
No, it'll be as part of the "Worldwide War on Terrorism" - taking out the PKK bases in North Iraq and the PKK enabling Barsani regime.
I don't see much of a reason to believe that the US would care in the least. They never have.