It will definitely have some effect. Why won't it? Even adding noise into prompts (like saying you will be rewarded $1000 for each correct answer) has some effe

It will definitely have some effect. Why won't it? Even adding noise into prompts (like saying you will be rewarded $1000 for each correct answer) has some effect. Whether the 'effect' something implied by the prompt, or even something we can understand, is a totally different question.