As someone who's been on his own journey with alcohol and hung out in a few sobriety forums (/r/stopdrinking is brilliant), I've seen a very clear difference between the 12-steppers and other people who are quit/quitting/moderating. I found the framing of the AA folks to be a lot more extreme. Problematic alcohol use is frequently described as an incurable, progressive disease. There's also this heavy focus on guilt…
I think AA "accidentally" provides people with strong community support - a basic need, the lack of which often leads people to... well, drink. AA fulfills that need, and maybe the 12 steps themselves don't work, but the community does. That's why so many people swear by it and have success with it. So yes, it'll be a little culty, because those are the principles of this particular community, but I think it's far mo…
I think you are on to something, which is that providing connection can help people to overcome addiction. (Or perhaps the reverse - that addiction can help people cope with a lack of connection.)
If AA is the only source of connection, then I imagine losing it might very well result in relapse simply from losing the connection itself (not to mention the encouragement to remain sober.)