I would doubt it to. But Erdogan is hard at work to make himself the new Sultan and purging everything in sight that's even remotly considered a threat to him so it will be increasingly hard to dispose of him.
The Kurds are truly one of the few that could seriously go against Turkey at this point. Putin and Assad both publicly supported them in fighting ISIS, I'm curious how much they are actually financing them. If Erdogan tries to start removing all Kurds from Turkey, that would be very very interesting how it plays out.
Erdogan is already in an active civil war against the Kurds in Turkey. His main reason to finally intervene in the ISIS conflict in Syria was to prevent the two northern kurdish fronts to connect and form a threat to him. He even shelled Kurdish positions while the Kurds where fighting ISIS. He supported ISIS for a long time with the secret oil trades across the border and offering them a market to. This whole thing is as dark as it is ugly
I highly doubt the US and UK would just simply let Turkey drop out of NATO. That is far too strategic of a location for them, with their locality to Moscow, Damascus, Baghdad and Tehran. If Erdogan makes a move to leave NATO, then I'd fully expect that the faux military coupe would get a strong revival from the CIA and GCHQ.