Their ancestors were citizens of Ottoman empire and their business exits because of Sultans patronage. Who knows how they feel about the connection, yours is only speculation.
Considering they received their start through the patronage of the Ottoman Emperor, I doubt that, else that element would have been erased from their history. Turks, maybe not, but Ottomans they were.
They moved the business to the US before the genocide though (and in good time too!), so not sure how they would have been affected.
