“Is yoga a good way to get rid of an addiction?”

Very insightful of you. In the past twenty years the professional medical field has suddenly become aware of the age old practices of yoga and meditation. Both have been shown to be of significant benefit in treating medical maladies.
My belief is that like all of us, anyone with a medical condition prefers to NOT be told what to do. Offer a suggestion or invite brother to consider the option of one tool amongst many that helps treat many medical conditions. Let him explore and decide, usually better chance of his accepting.
Than-you for the empathy and concern you have for brother. Be patient and kind- he will need lots of love and support to change his life pattern.

It could but I would advise abstinence from alcohol first

Not much good research to prove it helps, but it certainly may help some people. alcohol is quick and reliable way to relax, Yoga takes practice and patience (which many addicts dont have much of) and is not as fast as alcohol. so most addicts prefer to drink alcohol to relax. Substance use disorders are complex conditions where there is loss of control of the ability to reliably stop excess alcohol use. Recovery is multifaceted and patients can benefit from professional help, meds (like naltrexone) AA, individual and group counseling as well as fellowship with others struggling with the same issues.

No, not in terms of his drinking problem. Treat the drinking problem and then he may benefit from Yoga.