Is there any evidence that it was chosen by the Ottomans because it had a Graeco-Roman past?
The Crescent and Star used by contemporary Muslim nations comes from the Ottoman red and white star and crescent flag that first appeared under Mustafa III (1757-74). As a symbol, the star and crescent existed long before the Ottomans adopted it, but there is no explicit reason why they chose it. The crescent moon, by itself, was a popular Turkic symbol on its own prior to the Turkic migrations to the Middle East. The crescent and star were also somewhat prominent symbols for the Byzantine Empire.