Well, according to Wiki, Cordoba stopped being a real "Republic" by the time their second ruler, Abul Walid, abdicated in favor of his two sons. Who, of course, squabbled with each other for the right to rule the city, giving the Mutamids(Abbads) of Seville an ample opportunity to annex the city into their taifa emirate. That being said, I don't see why Paradox would make them unplayable just because they weren't a Christian republic.(Providing you've got Sword Of Islam installed that is.)
I for one would love to play as them. It would be like an Islamic version of the Rise of Rome!('cept in Spain,) Imagine, marching highly disciplined Ibero-Arab armies into the heart of Europe, bringing classical literature and the True Word of The Prophet to the heathen barbarians of the North!(Providing you survive the Reconquista that is...)