I don't
think so. Nanamo didn't even go to the Seventh Astral Era ceremony in Mor Dhona, if I remember correctly, and, often, either Raubahn handles her affairs or the Syndicate just blocks them; not really hallmarks of someone with control over an Alliance. Ul'dah
is bankrolling a good chunk of the Alliance affairs, however, and, geographically speaking, it's between Limsa and Gridania. We debated the Ul'dah location
once upon a time and I remember one of the strongest points being that, until 3.0, we never saw Nanamo leave Ul'dah at all. The Ishgard speech might actually be a hint that, as the post-ARR changes to the status quo, she has much more freedom. Lolorito wants control, but he doesn't want to bear the burdens of rule. He's a bad figurehead and he knows it.
The Alliance itself
seems to be led as a council, with each leader handling their own nation's contributions. I'm not sure it, as a singular entity, has a singular leader.