Actually, I don't believe that's the case.
The main difficulty for recovering alcoholics is that they have not learned proper responses to life's challenges, because they responded to every challenge by using alcohol. And when that response is taken away, they don't know 'how to live'.
And most alcoholics become alcoholic at an early age, further exacerbating this problem. I was 35 years old when I finally quit drinking, but I had started drinking in my early teens. So I had not learned a proper way of dealing with nearly every aspect of adult life. Once sober, I was 20 years "behind" everyone else in terms of life-skills and emotional development. And I was scared to death of everything! I wasn't depressed, I was just flat out confused, and frightened. And I found this to be the case with most of the recovering alcoholics I associated with. Though few of them would admit to that, and many would have gladly accepted the diagnosis of depression rather than to admit that they were just mentally and emotionally retarded, and so were just afraid and confused.
My solution to a flat tire was to get drunk. My solution to not having the courage to ask a girl for a date was to get drunk. My solution for having to pay my taxes every year was to get drunk. My solution for anything that happened to me was to get drunk.
And it's not just the bad stuff, it's the good stuff, too. Something bad happens, drink it away. Something good happens, celebrate it by drinking, because everything is better when you drink! Nothing happens, drink to the boredom and soon you'll be having fun! Drink, drink, drink. The solution was always to drink. If I had been depressed, I wouldn't have known it, because I was always drunk. And even after I sobered up, all depression would have been to me was an excuse to get drunk, again. I couldn't afford it.
To be honest, recovery is a pretty simple process, though it's not easy. Basically, you just have to surrender to life, and to your own emotions. And stop trying to control them or deny them with chemical substances or other forms of distraction and manipulation. Instead, learn to live with them. Deal with them. And finally, to let them go.
Depression is a luxury that few alcoholics can afford to keep around.