Wondering if I can recycle some of my Crusade era Saracens as Arab Conquest.
Yes, some did - http://www.iranicaonline.org/articles/amama-or-ammama-arabic-emama-the-turban - but perhaps more for chiefs than commoners (https://books.google.co.uk/books?id=SxPyHsFzNMIC&pg=PA64&lpg=PA64&dq=origins+of+arab+turban&source=bl&ots=xE5qQLPdW7&sig=R_WRNeEtAq_Owl-jyi7sI0q8vhU&hl=en&sa=X&ved=0ahUKEwiriabNsfHTAhUHDsAKHR9KAz04ChDoAQgmMAE#v=onepage&q=origins%20of%20arab%20turban&f=false), and whether it was quite the same style of turban as later, I do not know.