More important question here is, is EU willing to failing to integrate Turkey at the whim of Greece and Greek Cypriots.Do you want to miss this opportunity to integrate with Europe because of Northern Cyprus?
Annan Plan was supported by Turkey, Greece, US, EU, UK and UN. It would oversee a token Turkish force on the island, which would be reduced to 500 in 5 years at most and a complete withdrawal in 10. All the political machinations of the plan was so that the majority wouldn't try to bend the minority's arm around its back again, as it had done so after 1964. Greek Cypriots were awarded with an EU membership for their nay vote. Turkey was ready and willing to get itself rid of the Cyprus problem then.
Turkey was once again very willing and pushing for peace in 2017 in Crans Montana. Greek Cypriot side was again the side that refused any talks going forward. Because crux of the matter is that Greek Cypriots are fine and happy with having 100% control of their part of the island and we now know that they are not interested in sharing power.
Trust is long gone there.
"Greece, Cyprus, Enosis" was written on every single Cypriot army base's entrance until 1974. It's still shouted by both Greek and Greek Cypriot militaries as a chant, a horrible way of showing their ideological training. No government worth its mettle is abandoning Cyprus. Not just because of history or humanity, but also because it's literally our belly and backyard.
Settlers that have now become Cypriots are not going anywhere, army is not going anywhere. All the implied threats are nice and all, but we've seen far worse. We survived Assad and Russians on our ass, we can survive the EU.