Anecdotally, I get a lot more captcha's when it's turned on. I regularly log in to sites and get prompts telling me I need to enter email confirmation codes. I signed up for a service recently that auto locked my account immediately on signup because of "abuse detection".
To be clear, I take those as positive signs. My rough metric is that if privacy invasive sites are mad at me, I'm probably doing something right. So that's certainly not hard proof that it's effective, but it's at least circumstantial evidence that websites that I know fingerprint me get irritated when I turn it on.