Well, yes, but also no. It doesn't NEED to be taught. Gun safety is only common sense - don't point at anything you don't want to destroy, don't keep them loaded, put the safety on. Those you don't need being taught. because if you are normal you can think of it on your own, so the only people needing classes for it are special needs.
Makes more sense to teach how guns WORK. That would actually improve safety more, because then you'd know the activation points of bullets and how to know if it's ring or center so you don't accidently fire an unloaded bullet into someones heart.