If you dry heave while you are running, you won't be able to breath. That is an essential component of being able to run faster.
As for your helpful NCO, I think he's a bit in the dark about the mechanics of exertion. Don't believe everything you are told. Some NCOs try to show they are hard and tough and will say anything to a young soldier. Anything said, needs to be of importance, not showing off.
PJ D-Dog