Columbus believed that he had reached Asia until his death (although some of his contemporaries already suspected that he had found a new continent). But could he actually have made it all the way around the globe if North- and South- America hadn't existed? Would he have run out of provisions?
He would not have. I discuss Columbus a bit more here but the most important takeaway you should have from the linked thread is that he miscaluculated considerably on distance. He believe the distance to Asia to be only 20 percent of what it actually was, and was in no way prepared for the undertaking of a journey to actually hit Asia if there were no Americas in the way.