The africa approach is likely, but the New World is not. Islamic Iberia was an erudite society, with access to greek works. They knew earth was round... but they also knew the western distance to Asia (Columbus was, plainly, compleyely out of his mind when he made his calculations; if he had not found a lucky continent on the way, they wouldhave died of hunger long before reaching China!) ´
The Spanish made the (insane) attempt for the same reason their Portuguese cousins made the not much saner African Circunvalation: The muslims blocked the easy path to Asia. A mulim Al-Andalus does not have that need, so America will go for France or England, for similar reasons than OTL Castille
It's a myth that Christian Europe thought the world was flat pre-Columbus; what they did not know was the distances to China and whether people lived south of the equator.