I would avoid saying anything to your employer about your alcoholism.
It's something that could so easily come back and bite you in the future. What if, months from now, you were late because of a traffic problem? What if you were having an 'off' day because you were concerned about a family issue? It seems that you would be leaving yourself open for your employer to go back to the alcoholism issue for any work related problem.
Is there anyway to have the discussion with your employer and not mention alcoholism specifically?