Freshstart-----the reason that he keeps coming around ----after you have have told him that you cannot have the drinking (that his life revolves around) in your life---is because he knows that he Can. He has made no move toward changing his actions, and you are still pretty much there in the relationship. He will, likely, avail himself to as much as you are willing to give.
Alcoholism is a powerful force within an individual and I doubt that not responding to an email would be enough to turn it in another direction. When pushed against the wall---alcoholics will chose the alcohol until and unless they make the decision to change their life. That is a major---Major---major expectation to expect from an alcoholic.
Your thought that he may be just waiting for someone to be honest with him about his drinking---seems a bit like Rebecca from Sunnybrook Farm thinking, to me. lol---Rebecca was a sweet girl, but a bit naïve to life's realities.
It is sort of like the girl who thought that the bull wouldn't gore her because she was a vegetarian.