I dunno how much Jeph is alluding to his own experience with alcoholism with Faye, but it's worth noting once again that Jeph. He had a very bad experience which served as a wake up call he had to quit. And then he decided to quit cold turkey, from what I can gather largely on his own. As far as I can tell, he didn't go into rehab. He didn't join AA. He had a few slip ups, but he's largely kept sober ever since 2011. There's no reason for him to make Faye's recovery similar to his own, but on the other hand, having gone through recovery, he knows that if you decide to make the change, you don't need all that external support pushing you. And I simply don't think it would fit the comic from a story perspective to continue to focus on Faye making terrible choices for a year or something.
The no AA thing I think is most important. Jeph is a pretty militant atheist, and you have to explicitly recognize your fate is in the hands of a "higher power" to be in AA. Jeph has said that if that's what someone needs to quit, that's fine. But he's also said he doesn't want to write a religious character, because he just feels religion is wrong. I think Faye has been established to be more blase/neutral about religion, but at the same time, I don't think Jeph would want to elevate a frankly religious organization in his comic, making people think that joining was a requirement if you want to stay sober.