From what I learned from hubby's therapists, Addiction is always considered the primary diagnosis and treated as such. Once the addiction is being managed effectively, other issues can be dealt with. Hard to get very far in treatment of other issues when active addiction/using is occurring. Of course there are many emotional issues intertwined, for example shame, self worth, values, lying, guilt, etc and part of the addiction treatment involves dealing with those issues as well. But if you have an addict/alcoholic and you just try to treat their issue if low self worth in hopes they will then stop being an addict, that is not likely to work.
All the best-