An LLM is just computer function that predicts next word based on the input you give it. It doesn't make any difference what the input is (e.g. please respond in style X) - the function doesn't change, and the statistical signature of how it works will still be there.

If you don't believe me, try it for yourself. Ask an AI to generate some text and give it to the AI detector below (paste your text, then click on scan). Now ask the AI to generate in a different style and see if it causes the detector to fail.

https://app.gptzero.me/