How can we know for certain? If he did, he didn't act like it. Or at least, he acted in a sense that his personal primacy was to be exercised only on an extraordinary basis. That is, he may have believed that to be the case, but acted and wrote in such a manner as to not draw attention to it. Personally, I don't believe he saw himself that way.
It's not too great a stretch to have thought that Rome would become an important place for the Church. After all, it was the capital of the empire. So I think the answer to your second question could very well be yes, he did realize that the church in Rome would become central, though I don't know about being the headquarters.
Becky