Back in the old days , Big Book points out, we alcoholics were almost never completely honest with our doctors. As a result they has a lot of trouble helping us. It's very hard to treat something when the patient is not telling the truth about the symptoms.
But, of course in this enlightened age alcoholics are much more honest with doctors that they used to be. And that is the key.
In my experience, those with a genuine mental illness can and do recover if they have the capacity to be honest. It may be a little more difficult, but treatment of the illness does not seem to be a barrier to a spiritual experience.
Then, as I heard a young woman share recently, when she was taking medication to avoid the pain of recovery (pretty much all spiritual and emotional growth involves pain) she found she had only postponed the pain, and avoided the growth. All the things she should have felt in the first few months began to make themselves known as she came of the meds. Of course, she explained, she had not been honest with her doctor. She blew us away with her honesty in the meeting.