Yes absolutely they would and insurgencies are not the same thing as two nations fighting each other. America has twice as many gun owners as there are people in Afghanistan, a large chunk of them have combat experience.
Civil wars happen all of the time. Not only is propaganda effective, but militaries have ways to mitigate this, like moving soldiers far away from home to fight in places they don't have familial/cultural/economic/etc ties, which also makes it more likely that the propaganda will work.