Gottalife seems spot on here. Substance abuse interferes with recovery or treatment from other so-called mental disorders. Getting sober is likely the first step in addressing PTSD. One could argue that substance abuse is the antithesis of constructively addressing PTSD.
So, can one recover from alcoholism whilst still suffering PTSD? I would say no because recovery implies something deeper than sobriety. In my case, for example, I have been sober for 15 months, and I am simultaneously recovering from addictions and trauma. I discovered at some point that my drinking had become an avenue to avoid facing the pain of past traumas - sexual abuse, physical abuse, psychological abuse, car accidents, witnessing death...
I know this: I had no hope of mental health without first addressing the addiction because the addiction is a symptom of my mental dis-ease. I drank because of the symptoms I suffered when I wasn't drinking. I cannot overcome those symptoms by numbing them. So, I had to get sober and feel the shame, the anxiety, the fear, the horror, the disappointment, the embarrassment, the nightmares, and the pain before I could learn to love myself again and learn to have compassion for myself and for others, including those who have done me harm.
Trauma and stress only enter the realm of disorder when they affect us to the level that we are dis-ordered; when we are not functioning at a level one would expect of an otherwise healthy adult. Alcohol helped me relax, sure, but eventually it contributed to my dis-order and to my mental and emotional dis-ease.
I guess I'm saying that recovery from alcoholism or addiction, at least in my case, is inextricably entwined with recovery from the traumas I have endured. Recovery for me means recovery from all of it - addiction and trauma. I'm not sure what that will look or feel like, but I sense I'm getting there, and it's not about no longer feeling pain. I think it's about feeling pain and accepting it.