Eh… sort of? In a sense, they become less accurate, because the prediction market is the causative event, not an independent observer.

Not really, for the same reason entrapment isn't usually seen as an accurate way to gather information for law enforcement. See also Goodhart's law and overfitting.

"You provide the gambling, I'll provide the war"

Until the tail starts wagging the dog.

As long as we realize that prediction market accuracy is not all we care about.

See also: one can have very high economic efficiency with very high inequality, war, disease, misery, etc.