In the US (where the dealer with the chatbot is), manufacturers sell cars to dealers, and dealers sell cars to customers. (Tesla bypassing this arrangement was a big deal at the time, but I can't remember how that turned out.)
So in this case it would be between the customer and "Chevrolet of Watsonville", but were someone to take it to court, the court would probably find that one of the requirements of contract, "meeting of the minds", was not met -- or that the website (including the chatbot) was an invitation to treat, not an offer, since the contract process for car sales is standardized.
Practically speaking, no. It would be huge news in the legal field if some court allowed it, and the decision would certainly be appealed and overturned.
