Cockroaches are everywhere , even in Turkey. The Turkish cockroach is not a particularly aggressive indoor pest, but it can cause a lot of problems. It brings a number of health hazards indoors, such as fungus and bacteria. These cockroaches are most often found outside, in areas where food waste is plentiful.
It seems that at least in the tourists areas in Turkey the cockroaches are not a big nuisance and you shouldn’t worry about it.