A big part of Dada's pull was on the carpet of "art status."
How is it that we come to call something art? I think most people need it to fit with their assumptions about "what art IS." Assumptions learned largely out of awareness and perpetually thereafter kept out of awareness. By flipping over a urinal, signing it, titling it "Fountain" and submitting it to an art show which promised to show all work submitted, Duchamp revealed what George Dickie calls "the institutional essence of art." What makes this relevant to social movements is clarified by Dickie:
"[Philosophers of art] entirely ignored the nonexhibited property of status. When, however, the objects are bizarre, as those of the Dadaists are, our attention is forced away from the objects' obvious properties to a consideration of the objects in their social context."
Linguistic nonsense, even such that goes as far as being anti-communicative seems to be running along a parallel intention. As the anti-art of the Dadaists aims at your definition of art, anti-communicative "language" aims at your sense of communication and linguistically constructed reality, but also helps define it. The white space around the letters you're reading is just as important as the black lines that form the letters and separate the words.
As an intentional utterance anti-communication still communicates just like anti-art is still art. It just says something like, "I don't want you or myself to understand me in a rational or conventional way, if at all right now. Perhaps I'm just curious as to what it will be like to do this around other people. Perhaps I'm more curious as to how this demographic will respond. Perhaps, I'm just interested in what will come out of my mouth."
By inspecting nonsense's context it unfailingly can be observed as non-arbitrary, defining, and utterly meaningful. Nonsense could be done anywhere in any way with any medium—the fact that it was chosen to be done THERE, AT THAT TIME, with THAT MEDIUM, THAT WAY, means something. Though all efforts may be made for True nonsense to be created, unconsciously many choices get made that were not as purely arbitrary, irrational or chaotic as the intention may have been. It's just not possible for people to completely escape their intentionality, unconscious drives and socially created idea of "sense." The most sincere efforts to do so still leave behind traces. It seems the nature of these traces are what the Dadaists, Situationists, and Pinealists are most interested in.