> For example, Google can figure out if you are a bot with its "I'm not a robot" checkbox. This means that they can probably also figure out that fake automated requests are indeed fake.
Not necessarily. Given a noise script doesn't have to run unattended, the script could easily just prompt the user to solve any captchas it encounters, so that couldn't be used to distinguish real from fake.
Websites could have hidden captchas. For example, a website could track the movement of your mouse pointer and compute whether the movements most likely correspond to a human or not.