Not especially. Depending on where you set your standards for "holding a conversation" you can satisfy the requirement with a classical markov chatterbot, a well-trained parrot, a copy of Eliza, or a telemarketer flowchart drawn on a sheet of paper. Only the markov bot is made out of "weights" in the sense of a statistical model.

Parrots are intelligent animals, albeit with a limited capacity for vocabulary and syntax compared to a human, and Eliza and the flowchart are made out of explicitly encoded rules and conversational tactics.