It certainly would but that government wouldn't put themselves on the line like that.
Done it (or certainly not dissimilar things on the diplomatic front) before, could well do it again. Public opinion would certainly be behind them, and don't forget that the current Turkish government is busy turning away from the EU/US and realigning with the Middle East. Show me a better way to prove your leadership credentials.
http://en.wikipedia.org/wiki/Turkish_invasion_of_Cyprus