Churches...social connections...a feeling of belonging...if a person overindulges in booze it could be due to a loneliness or need for emotional support. A church can provide this....so it could be a good thing in the scenario presented.
Pick the low-hanging fruit
Re: "You don't have to be a believer to believe that it can work" It's confusing. Many non-believing alcoholics sober up in the atheist AA groups. Whatever they choose as their "higher power" works as well (maybe better) than belief in the supernatural.
Must be the psychology in the literature (tested/tried science) or easier to have faith in the universe, the moon, the blue chair - whatever.
Some of the more dangerous cult members and leaders I know of are ex-bad boys that have been steered to the 'light' by well-meaning victims of the cult that recruited them.
...isn't low-hanging fruit more susceptible to disease and contamination?