Currently we do nothing if no text is input in the form - https://github.com/vercel-labs/ai/blob/fd69e9a5628d1cd21a7c4a36584b4c577e0cc0a6/packages/core/react/use-chat.ts#L253

But, submitting a new API request without adding a new user message is a good way to get the LLM to continue its previous response, for example if the user hit stop, or the previous response reached the token limit. This is how the OpenAI playground works.