The two articles linked to at the bottom talk about multiple years, the third link points to a news article that refers to some research that uses one year as a minimum.
This feels more believable than "a few months". My flat mate has ADD and has phases during which he's clearly addicted to alcohol. At one point he stopped drinking completely for over 6 months, but drank a small amount once and things spiralled out of control again.
He does view addiction as a personality trait (in part because he knows that people with ADD develop addictions more often), and that attitue actually seems to help him. These days he abstains from addictive things because he "knows" that he'll get addicted to them once he starts.
I believe in the thesis of this blogpost (that addiction is in fact an emotion regulation problem, and that it can therefore be cured), but the approach my flat mate takes these days works pretty well, at least for the first year.