Is it free software?

I was referring to an LLM that is trained entirely and solely on the GPL'd project and no other corpus. Such LLMs generally don't exist, and may not be feasible to create at all.

But, of course, there is more to machine learning than LLMs. You could train something dumber on a single project, and perhaps it would be useful for some narrow task such as correcting indentation and other stylistic problems (when used in combination with a language server and other non-AI supporting infrastructure).