Being convicted of a DUI is not a typical exclusion in an auto policy so yes coverage should be afforded to the terms in your policy. Normally claims regarding an accident that took place while you were driving under the influence are generally covered by the insurance coverage you had in place at the time of the incident.
There are some states which have alcohol exclusions, but this is normally in regards to injuries one sustains while driving drunk.
Alcohol exclusions within insurance policies permit insurers to deny coverage to people injured while under the influence of alcohol. Exclusions can be used to deny payment to medical payments to doctors and hospitals. Some states laws are more lenient (requiring proof only of alcohol use prior to injury) and others being more strict (requiring proof of a causal relationship between the use of alcohol and the injury).
In the first half of 2007, legislation to repeal alcohol exclusion laws introduced in California so you can check with the CA legislature or Department of Insurance to see if CA has changes any laws regarding this topic.
To make certain that your insurance company will accept your claim for the vehicle that totaled at the time you were cited for a DUI, you should read through the terms of your policy and speak with your agent. Your agent should be able to advise you if there are any exclusions in your policy that would allow your insurer to deny your claim.