The question is: if we keep the same context and model, and the same LLM configuration (quantization etc.), does it provide the same output at same prompt?

If the answer is no, then we cannot be sure to use it as a high-level language. The whole purpose of a language is providing useful, concise constructs to avoid something not being specified (undefined behavior).

If we can't guarantee that the behavior of the language is going to be the same, it is no better than prompting someone some requirements and not checking what they are doing until the date of delivery.