That is a great idea.
Personally I have tried to serve bad data to google captchas for many years. The text capthas were really easy, but the newer image captchas are much more obstinate. Or maybe my shadow profile just got tagged as an unreliable captcha form-filler.
Smart, I think I’d have more success trying this than just leaving the situation entirely. This is going to be a lot easier to pull off with non tech oriented friends than a speech about privacy and why I have to leave the room.