I don't think it would matter if there were an Orthodox bishop in Rome, really. It wouldn't be a big deal like when Rome took half of the population of Antioch, for instance.
I think it would, however, make the Orthodox look silly so that's one consideration against it. It would obviously be done to spite the RC's.
Rome removed its titular Latin patriarchs of Constantinople, Alexandria, and Antioch (which it had in addition to the Uniate ones), which I see as a sign of good will, leaving only a Latin patriarch in Jerusalem where there is a Roman Catholic flock. Still, it would make sense to reduce him to an Archbishop since he doesn't have any real patriarchal powers. Still, that's for RC's to decide and not us.
So Hypo, if you wish to push for an Orthodox bishopric to be established in Rome, be my guest. :-)