I don't think alcoholism or addiction are diseases; but they're illnesses (mental illness); classified as such by the World Health Organisation.
And 'recovering' or 'recovered' are both concepts (abstract ideas), and are subjective.
For me, my drinking was just a symptom of a deeper problem which was a hopeless state of mind and body, and because I've recovered from that state, I class myself as a fully recovered alcoholic.
Yeh, I can't drink safely ever again, but so what? As I say, my drinking was only a symptom.