There are a variety of different models that are used. Some are the fully trained model, as per what National Service Dogs and ADI programs are doing.
There are some programs that are doing the owner-train participatory model. However, you must be aware, and it's highlighted in the prescriber guidelines, of the inherent danger of attempting to take a person with serious mental health issues, pair them with a dog of unknown provenance and get them to the finish line in the service dog world. If they fail, which there is a fairly large possibility of, you have literally reinforced failure for a veteran who is struggling. You can't have that.