In this scenario can you guarantee that the Kurds won't see an opportunity to carve out a small country of their own? Or that Turkey will not see a chance to once and for all remove a long time thorn in its side?
Actually it kinda depends on USA. Because the funny fact is US is ally both with Turkey and Kurds.
Turkey won't dare to expend the territories for sure, and also knows cannot do anything about the Kurds outside of Turkey, because they are tens of millions. A real Turkish-Kurdish war is the last thing both sides want because the Middle East is full of Turkish and Kurdish people without certain territories. Only in Iran there are almost 20 M Azeri Turks for instance. Iraq is another story, lots of Kurds and Turkmens live there.
As long as US doesn't fully back up Kurdish people they will settle with Northern Iraq and some around-areas they are currently living in.