The more compelling inversion is whether the likes of John Nash, Richard Feynman, John Conway etc could’ve had a lucrative second career as conmen.
Feynman for sure could have. In fact, I think he sort of did, although I'm not sure he meant to. Multiple generations of nerds now have taken books of his anecdotes varying in plausibility and obvious exaggeration as some sort of weird physics cult of personality gospel. But I don't think he was really setting out to curate his legacy so much as he was a good storyteller and he liked to entertain.
But could he have conned people on purpose? Absolutely.
von Neumann could. The others, I doubt it.
This is the real issue here. Those guys probably didn't become con men because they are humans with cares and concerns for their fellow humans. LLMs probably don't have those concerns. It is likely that some of the people in charge of or funding LLM development also do not have those concerns