I don't think so. People are just curious about strangers. Especially a tourist in a local kahve would be a big surprise if it is not a touristic town.

In a big city or in a touristic town nobody would care much. On the other hand, an ordinary traditional town or village would be very different.

I think what would happen is that, they would all think that you have lost your way and would try to help you. First they would offer you a seat. Then some tea and maybe water, afterwards some cigarettes of course. I think if you would talk a few words Turkish they would be so surprised that even people outside the cafe would come to see you.