I think that the advice for your grandfather to take a "familyfinder "test" is a good one, but keep in mind that any matches you may get will be muddled, so you will not know if the matches come from your grandfather's maternal or paternal sides.
No, you will not get results as specific as Greece or Turkey. Parts of the world are lumped in together under vague terms like "Middle East", "Scandanavia", "Siberia" etc, and Greece and Turkey being so close together there will not be any/much distinction between the two.
You may also find most of the matches will be with people living in America because they are more likely to have taken DNA tests that people living in other countries. I am not sure what the uptake is with people currently living in Greece and Turkey, but I would guess that it's fairly low.