Speaking as an alcoholic with many years of AA meetings, I don't think that I would conclude alcoholism from the symptoms you describe. If she was hiding booze, it wouldn't make sense that she leaves it out in the bathroom. Most alcoholics are sneakier than that.

Does she remember what happens in session? Or have good notes? If it is just a matter of her not remembering late night emails, I would do as she suggested and speak by phone rather than email. If sessions go ok, then I wouldn't concern myself with her seeming to be messy and ill. If sessions go badly, I would seek someone else. I don't think I would confront her based on the symptoms you have observed. It seems to me that it could be anything from simple insomnia and a messy bathroom to illness.