Absolutely, the pope (the Vatican) is incredibly influential, their organisation has tentacles all over the world. It's not so much about the faithful (but they do underpin the continued wealth) its about the power, it's about what they know and who they have access to.
When there's a new pope you will see all the major world leaders cueing up to see him, and they're not doing it for the votes of the Catholics (although thats nice), they're doing it for the favours and the influence.