Yes, assuming you had any in your possession, though I don't know about how common specifically Byzantine coinage was in the fifteenth century. But the mid-fifteenth century was a time of extreme silver shortage in Europe and the Mediterranean, and Mehmed II instituted harsh monetary laws in order to counteract this. All bullion had to be sold to the state at the officially sanctioned price in order to be minted into Ottoman coins, and the Ottomans employed agents to seek out illegally held silver. All silver export was banned, both bullion and coin. As a corollary they encouraged the import of foreign coinage and even allowed people to pay their taxes and fees in it. Presumably this included Byzantine coins as well. The goal was simply to get as much silver into circulation as possible and to prevent the hoarding which was becoming common at that time. The only coinage which was expressly banned was old Ottoman money. Mehmed II frequently debased the coinage in an effort to both raise revenue for himself and to increase the volume of coinage in circulation. For each debasement all Ottoman silver coins (akçe) were required to be submitted to the mints for renewal.

Şevket Pamuk, A Monetary History of the Ottoman Empire (Cambridge: Cambridge University Press, 2000), pp. 40-58.