Well, yes, it could.
It seems like Turkey would like to invade Iraq:
The possibility of Turkish military action in northern Iraq seems all the more likely now that the two countries have started negotiating the circumstances in which Turkey would not refrain from intervening, according to statements made by Turkey's special coordinator to counter the Kurdistan Workers' Party (PKK) terrorism.
It seems the U.S. is none too popular with Turkey right now. A while back, the U.S. captured some Turkish forces in the border region -- it is unclear on which side of the border -- and roughed them up a bit. The incident has since been the subject of a made-for-tv movie in Turkey, in which the Turkish soldiers were cast as handsome heroes and the Americans as, well, ugly bastards.