Being in an alliance is quite similar to being in a clique inside a larger guild, except that it feels more "legitimate" in a way since there is a dedicated structure for it, and in terms of gameplay benefits, the guild/clique is actually more important to you than the alliance.
Like with everything else in Neverwinter, I'm more casual about socialising in it than I am in my main MMO, where I've always been super involved with any guild that I've been in. In Neverwinter on the other hand, I don't even read chat most of the time, including the green guild/alliance chat. On the rare occasions when I do look at it I notice that the people who are talking are way more into the game than I am, though I also see the occasional newbie question which serves to reassure me that I'm not completely clueless.
One thing that's interesting is that there are a couple of names that pop up in alliance chat all the time, to the point that I feel I "know" them. There is Xtremoz, the alliance leader, as well as some players called Bron, Bob and Bab who just seem to be online a lot. They don't know me at all of course, but just seeing the same names in chat over and over again gives the alliance a sense of stability even for casual players like me. It makes me appreciate that even guildies that never or rarely talk might be quietly benefitting from reading guild chat, and that in my SWTOR guild for example, someone might well be looking at me as one of those always-around public faces of the guild that hold things together.