I read the original question as "is the 'Functionary' thing something that works with any LLM you can run in llama.cpp, not just only with the special 'Functionary' finetuned models?", to which the answer now is clearly no.
Very interesting question, as I also read top-level post as saying it's a llama-cpp-python feature, and therefore I could shove some random dolphin-mixtral or whatever I have on my hard drive at it, and it will work.