In retrospect, after searching for Alpha Centauri references, I think the following two things are most important:

- Aldebaran III is canonically a Federation colony (or Federation world). Technically, it does not imply UFP membership. Or at least, it implies the same unclear status that all major colony worlds like Vega and Mars share.
- Star Trek Maps lists Aldebaran (but also Vega and other similar worlds) as a Federation member. The majority of later unofficial materials support this.

So, it basically comes down to this: if you’re ruthlessly adhering to canon, there is no strict evidence any of the colony worlds are proper members. However, most (unofficial) works assume that at least major colonies like Aldebaran, Vega, Ophiucus, etc. are members. The lines are vague, however, as can be seen in Mandel’s Star Trek Charts, which lists a lot of (IMO far too many) colonies as members.

I don’t think Blish’s “Where No Man…” expanded on it much. It is interesting that he makes some twists to get McCoy off the ship and Sulu into the physics department, since he doesn’t take the now nearly universal approach that WNMHGB happened before any other eps (and in my mind, before the Five Year Mission). But that’s neither here nor there.