You don't ever know if he is going to drink. And chances are, even if he is, he is going to lie to you. But you will know when he does. They think they are hiding it, but they aren't. Go by what he is showing you, not by what he is telling you. Period.
Whether or not you want to stay with him is your choice, and I am there myself. I do not trust my boyfriend at all, and he knows it. But he is trying. Is it enough? I don't know. I guess I will either stick with him, or leave him. Either he will recover or he won't. Time will tell.