Incorrect. Propaganda is not a form of discussion it is a form of deception. All it does is invoke an emotion and offers no substantial logic or reasoning against which to argue. Just like Jingoism it is very hard to argue against something like "do you support our troops?"
The problem isn't with the left or the right using propaganda laced songs, the problem lays in the fact that they hurt actual democracy by muddying the actual discusssion.
Rosie the Riveter would disagree with your assessment.