I'm a lowly PhD student who's not yet formally taught a class, but here's my initial reaction: Chat GPT can be used for coding/data cleaning purposes (when necessary), and it can also be fine for spell checking. However, where I sort of would draw the line is them formally using it to write the paper. The paper should be the student's work, not Chat GPTs work.

I don't know how to check if chat GPT's been used, but that's my view on it. As someone who writes code for statistics purposes, GPT can be quite useful for a variety of problems (not that I've used it). But, it should not (nor should we expect it to) replace the human analysts, and that philosophy matters in the classroom too. In other words, it can be used as an awesome supplement to one's work-- never as a substitute. So, I think your idea is just fine, so long as you can check to see if it was used and how. The main thing to be concerned about, I think, is how to know if someone actually did use it, but did not disclose it. I'm sure people who have worked with it would have a better idea than I would.