Yes.
It depends on lots of factors though. The alcoholic really taking recovery seriously and the non-drinker being patient and knowledgeable about the disease (not getting lost in it or having it control their life).
Communication and establishing healthy boundaries need to be in place as well. But like any relationship, what works out in the long run depends on so many variables outside of coping with alcoholism (having the same goals, shared interests, respect etc).
In active alcoholism though, all bets are off and even the strongest of relationships will be challenged.