Of course there are. Once having completed whatever initial treatment regimen is prescribed, these "alcoholics" are referred to as "recovering alcoholics". The same applies to drug addicts too. Some of those suffering from other psychological "abnormalities" are still eligible to fill safety sensitive positions as well. And not just in flying either. I'd go so far as to say that every major career field is probably represented.
AA purloined the word 'alcoholic' and redefined it for AA purposes, and introduced the term 'recovering alcoholic'. The 'disease' concept is not universally accepted but alcoholism is recognised as a mental illness. AA maintain that alcoholism is incurable hence 'recovering', never 'recovered' so any programme that is AA based (12-step) is for life.
Flying airlines is particularly dangerous to alcoholics:
Long periods of boredom
Periods of high stress
Missed, delayed or snack meals
Overnights alone without spouse or partner
Sufficient money to spend
An unusually (compared with other occupations) high proportion of young-ish, fit-ish, attractive-ish people who are all away from home and glad of company...where does one meet...over a meal or a drink.
The acronym HALT is used in some treatment programmes to remind alcoholics of the danger times --
Hungry
Angry
Lonely
Tired
These should all be avoided as far as possible as they are triggers to have a drink.
The best thing an alcoholic pilot can do is find a non-flying role where the hours are regular, meals are regular and they can go home safely to their partner every evening. The best thing an airline can do for an alcoholic pilot is find them an appropriate ground job.