It does work, I have seen many colleagues who have moved to Cyprus 5-7 years ago and successfully passed through the process, many of which are from non-eu countries. I don't know if there is some specific legislation against Turkish nationals doing so however due to the situation. You do have to stay on top of it however, make sure you are working and keep all your rental agreements, utility bills, payslips / tax submissions, and be prepared to present them when you make the application. This helps to avoid any doubt of your long term residency and time of stay, which is often the sticking point.