Psoriasis Is a disease, or do you doubt that as well? Would there be 95 living sufferers of psoriasis and 95 dead diabetics? Probably. Does that mean psoriasis is not a disease? Don't be a dope.
You didn't mention if there'd be unlimited access to alcohol on the island. Would your numbers remain he same provided there were cases and cases of liquor there? The disease is only active when alcoholics are actively drinking (also, there's no such thing as a former alcoholic...although I am not an AA supporter, one area we do agree is "once an alcoholic, always an alcoholic").
My understanding of alcoholism is that the alcoholic processes alcohol much differently than the non-alcoholic, which is why the alcoholic mostly cannot stop once he starts drinking. If that's not a disease, I don't know what is.