It sounds like you want to protect the possibility of drinking again in the future. Like, if they know that you’re in AA, then everyone will be judging if you do take a drink. But if you’re never going to drink again, why is that a problem?
Second, let’s say you do go and you relapse. Your boss’ BEST FRIEND is in AA, so chances are that your boss knows a bit about the road to sobriety. Don’t you think that might predispose him to be a bit kinder and more forgiving to you as you seek yours?