AI training is not automatically not fair use. Nor is it automatically fair use. But it can be. And if used for such a "parody" that does qualify, it stands to reason that training the AI for that purpose would also fall under this.
Aside from the work, there is no substantial difference between an arist made of flesh to copy and plagiacaricaturize another ones ip, or to have an AI do it. The ip still gets transformed into the parody.
fair use is about result, not about method.