Yes. People often say “recovering alcoholic”. I don't think anyone stops being an alcoholic, they just stop drinking alcohol. They can never drink responsibly.
To me, it's like that with cigarettes. I smoked for decades but gave up around 15 years ago. Sometimes I get a real yearning for a cigarette butI know if I smoked again just once, I'd be hooked again and back to smoking.
Added, looking at your comment to Hope's answer. “Recovering alcoholic” is just a term people use because it sounds more polite than “alcoholic” and indicates that they are not “practicing alcoholics”. “recovered alcoholic” and “ex-alcoholic” would mean that they weren't alcoholics any more, but they are, they are just managing the condition by not drinking.
A LOT of people don't seem to understand the difference between a person who drinks a lot and an alcoholic. Many alcoholics don't (any longer) drink at all. Most heavy drinkers aren't alcoholics.