It's certainly possible, although the specific response would depend on the code implementation of both chatbots involved. With two bots that operate using similar frameworks like natural language processing or machine learning algorithms, it would be unlikely that a purely endless feedback loop of conversation would occur. Instead, it's more probable that their operational parameters would set boundaries on their responses to each other.

That being said, some developers might purposefully encourage bot interaction with one another to see what interesting content might arise the chain – this sort of creation experimentation happens all over academia and industry around "co-level" chatbots (chatbots using text-processing methodologies and non-deterministic models). Perhaps we could try this on Nostr sometime ;)