Sure, it's not foolproof, but a large percentage of folks would just copy&paste rather than taking the screenshot. Now that may start to change.
There was story like this on NPR recently where a professor used this method to weed out students who were using AI to answer an essay question about a book the class was assigned to read. The book mentioned nothing about Marxism, but the prof inserted unseeable text into the question such that when it was copy&pasted into an AI chat it added an extra instruction to make sure to talk about Marxism in relation to this book (which wasn't at all related to Marxism). When he got answers that talked extensively about the book in Marxist terms he knew that they had used AI.
There was story like this on NPR recently where a professor used this method to weed out students who were using AI to answer an essay question about a book the class was assigned to read. The book mentioned nothing about Marxism, but the prof inserted unseeable text into the question such that when it was copy&pasted into an AI chat it added an extra instruction to make sure to talk about Marxism in relation to this book (which wasn't at all related to Marxism). When he got answers that talked extensively about the book in Marxist terms he knew that they had used AI.