you dont need to make the decision about a final breakup just yet. If you want to give him the chance then maybe its good if you say to him not to see you for 3 weeks or so and then you meet him again and talk. If feelings are still there you can go from there. If its real you will not loose him - you are probably the only one that helps him and after being sober for three weeks he might realise that.
I have not specific experience with alcoholics though I am from a psychology background.AA meetings arent the only thing out there for help and I dont neccessarily think they are the best option. Maybe your bf would benefit more from personal counseling to work on those problems that are underlying the need to drink.