More importantly, though, Curzon was a Federation diplomat for decades. Now foreign-born state officals aren't unheard of (Henry Kissenger and Madeline Albright, for instance), but seems pretty unlikely.
Why does it seem so unlikely? You would think that the "enlightened" Federation would care little about whether someone was born a Federation citizen or became one later in life...unless they were partly Romulan.
That said, I think the Trill are members and the writers intended them to be. You think that if Jadzia had to go through the processes to join Starfleet that Nog did they would have had her involved in Nog's journey in some way.