I would imagine largely the same as narcotics recovery programs happen in places where narcotics are banned. The reason you think of AA as distinct from NA is because you live in a place alcohol is legal and easily obtained. If you're in a place where it isn't, it's just another illegal drug, and there are recovery programs for illegal drugs. I would imagine it being banned simultaneously makes it harder to find recovery programs and harder to develop dependency in the first place, which sounds like it would roughly cancel out.
That's an interesting way to look at it. But alcohol there is not just illegal, it's a religious commandment and mortal sin (I believe), Much more serious.
So are narcotics elsewhere. This is a difference of degree, not type. Black markets exist everywhere. Again, I would suppose that the difficulty in acquiring alcohol and the difficulty in acquiring recovery aid largely cancel out. Alcoholism is much less pervasive in places without bars and liquor stores.
I would say yes it's a matter of degree. I think alcohol in Muslim countries is looked down on much worse than narcotics in the West. Alcohol is a sin, a temptation, that you have to steel yourself against, that good Muslims don't do and bad Muslims do.
Narcotics in the West is usually seen as a result of drug prescriptions, addiction, and the root cause/problem is commonly sympathized with. Something that society wants to help people out of. (I'm not sure how narcotics are seen in Muslim countries.)