Cobra seems like such a lightweight that he'd get fucked up on much less alcohol than it'd take to really "become an alcoholic". He obviously prefers living with a buzz and will function... "normally" when not.
I think it's more of a case of realizes what a loser he is and it's embarrassing when sober, so he stays drunk. And that's still an "alcohol problem", but I don't see him dropping like Amy Winehouse any time soon. I think his biggest non-liver damage (which'll take a bit longer to knock him out) issue with the dranks atm is him eventually gaining enough liquid courage and the unfortunate timing of an angry, hillbilly neighbor demanding he quite the fuck down and having an agitated, boozed up chimp boy attacking him and getting pummeled by someone who's likely not going to be particularly sympathetic that he's a retard and really let him have it.