Look, it does not matter.
The definition of "illness/disorder" is not relevant. Neither of us is a medical doctor och researcher. What the fuck do we know about delicate matters of DSM-V?
The AA was always meant to be a self help organization. They tried with rehabs and failed, hence they never do that again.
Read the litterature, it clearly states that the biggest problem is the behaviour and thought process of the addict. Once you change that with the help of a structured program and higher power to some extent, you'll be fine. Tons of people are ateists in AA and do not think of alcoholism as a disease. They even have half the books with many personal stories of people who don't believe in any God. Sounds close to CBT to me.
My only problem is when the state forces people to go to a self help organization, it defines the purpose. That is only because AA is free, of course and Americans hate to pay taxes to finance proper treatment.
Also, people always frown upon "once an addict, always an addict" yet seldom have any examples of people who were fiends and then all of a sudden can control their intake. Look around the bad parts of your own and see for yourself the opposite.