There is no such thing as a healthy addiction, it's just that some are more unhealthy than others.
You say he is a recovering alcoholic? To what degree? Is he just going cold turkey? Is he being helped by CDAT or similar? Is he on meds to combat the effects of alcohol withdrawel? Was he a functioning alcoholic or nearer to the sterotype of park benches and cans of special brew? How long has he been dry?
All of those questions are relevent before anyone can even begin to offer an opinion.
But one of the big problems that many recovering alcoholics have is that drinking was their social life and took up much of their spare time and they need something to replace that. Running quite easily could and would fill those voids and longterm there is no reason why ultimately they shouldn't but in the short term it could still be a bad idea.
Edited: 05/01/2013 at 15:02