The martial arts (karate, judo and etc.) are a source of self-discipline instruction that don't require joining the military. Professional counseling to learn why he doesn't have self-discipline now is another option.
The military teaches discipline, that is true, but it is not really "self" discipline, it is imposed from without. As soon as your son left the military, he may not have any more self discipline than he went in with.
If he wants to learn self discipline, there are many other, much safer ways to go about it. I'm sure there are classes and counselors that specialize in it, plus innumerable self help books on the subject.
I favor the martial arts though in your son's case. His mind already has military in it, and being flung through the air or knocked to the ground in practice has a way of bringing light to a person's mind. Plus the classes are all about self discipline, the exercises, the movements, the practices,
If he insists on the leaving home part, suggest the Peace Corps. It's as bad conditions as the army but without the guns.