Just barely conceivable, being that the Barbery Pirates (and the Sale Rovers) raided as far as Iceland and South America from ports in Morocco and N. Africa, once they used captured or renegade Europeans to build blue-water ships capable of traveling great distances away from the coastlines. So, after the early 16th Century. Slaving would be their primary motivation.
Any attempt by Muslim (or any other) pirates to attempt to capture and hold an island territory would probably generate a lot of attention from the colonial governments of the area, I'd imagine. They should link up with the other pirates operating from Tortuga to have a good run of it.
I'm pretty sure there were Muslim pirates mixed up in the stew of multi-ethnic 16th and 17th Century piracy, anyways, OTL.