How are you defining productivity? In my experience veterans do have a vastly greater capacity for buckling down and grinding through, in a way that people who have not had military service do not. However, on the flip side, I’ve also seen the failure mode where veterans assume that buckling down and grinding through is the only way to solve a problem, rather than stepping back and considering the broader picture. From what I’ve seen, it takes some time for veterans to realize that, in the civilian world, orders aren’t absolute, and that if something doesn’t make sense, you have an obligation to question it, rather than to just grind out the work.
In the military, there are strictly prescribed procedures for how certain things should be done, and deviation from those rules is punished. In the civilian world, not only is deviation not punished, but it can even be rewarded, if you find a more efficient way of accomplishing the task.
Therefore, while I agree with your friend that veterans have greater self-discipline, I disagree with the assertion that this would lead to greater productivity. It’s plausible to me that the improvement in self-discipline is more than canceled out by the increased fixation on following rules and procedures unquestioningly.