.......Wouldn’t Turkey be searching for the Ark if they thought it was there ?......
Hunting the Ark is a profit center for Turkey. Why spend money to look for something not there when foreigners will spend good hard $$$ doing it for you.
Turkey is mostly Islamic and would not be agreeable to anything that would be remotely be considered ‘Jewish’ or ‘Christian’.
They would probably consider the Arks discovery more supportive of Jewish/Christtian theology than Islamic theology and therefore a threat to their culture.