OK, important disclaimer: I do not have professional knowledge regarding the biology or psychology of alcoholism. Whatever I say next is based on information I trust, but not information that has hard scientific data behind it, and it's information that I am not able to verify.
That being said:
I used to listen in to a weekly radio broadcast on a Polish radio station. The broadcast is half music, half stories and experiences regarding alcoholism. As the guy who runs the broadcast says every week, he's a long-time alcoholic, and he wanted to talk about his experience. So he went to the radio station and said "hey, let me talk about this". And they let him.
(I'm relaying the opening almost verbatim - well, except that "it's in Polish" part)
The broadcast alternated between taking calls from listeners (alcoholics, their families, friends) and talking to people who have had professional or semi-professional experience with treating addiction (to alcohol or drugs). That included doctors, workers at rehab centers, etc. It's also my strong impression the man running the show, in addition to having had experience of alcoholism firsthand, also did his homework on the effects of alcohol and how it is handled when trying to manage addiction.
One thing I remembered being said over and over and over again in the broadcast is this: alcoholism is a disease, it is an incurable disease and it is in the end a fatal disease. You can live with it, but it never goes away. This was repeated ad nauseam, to the point of almost being a mantra. Callers and guests to the show said things to the exact same effect. According to the broadcast, alcoholism is not something you recover from, not something you can cure, you can only opt to stop drinking. The most memorable thing about the show was that the guy running the broadcast introduced himself, every single time, as "I am [name] and I am an alcoholic". I happen to know a guy who is family with that man, and from I gather he has been clean for years and years now. But this very matter-of-fact and direct "I am an alcoholic" that was said every time is still something he decided to share with the audience every single week.
So, I don't have medical data regarding addiction, but if what I heard on that radio show is accurate, there is no such thing as fully recovering from alcoholism so that you can go back to drinking. You can be an alcoholic and function, you can be an alcoholic and appear to function, or you can be an alcoholic and it will damage your life and one day kill you. Both the explicit things said and the general vibe of the broadcast was that if you are an alcoholic and still drink, you still have a problem even if you appear to function OK. It may not kill you or ruin your life directly, but you're still not completely fine.
I thought I'd share this, I'm sure there's someone from the forum who has more grounded information regarding the medical side of things, but it appears to many, many alcoholics who decided to speak their mind on the show, it's either "drink" or "control your problem", with no real in-between.
And once again, take what I wrote with a grain of salt, I have no firm confirmation of this. But the stories I heard and the talks they had were very convincing. And they do mesh with the addiction problems I've seen in members of my close family and friends (mostly not alcohol-related, although it's there, too).