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Dude, Not Funny! is In-Universe Examples Only, so you shouldn't be listing such an example anywhere, unless a character in a work has that reaction to the parody you're describing.
As for whether it can cause that reaction in general... well, that's subjective. Maybe someone will have that reaction, maybe some won't.
Would it count as an example of Dude, Not Funny! if someone were to play around with a Tear Jerker moment? (i.e. if someone were to take the scene from My Little Pony: The Movie (2017) where Twilight attempts to steal the pearl and add in the Palpatine "Do it!" meme from Revenge of the Sith, would that evoke a Dude, Not Funny! reaction? Something like this: