Yes, but that's a poor signal. If only two users add "enough" noise to their signal, fingerprinting will only be able to proof a user added noise, but not which user did so. For a single site doing the fingerprinting.
Compare that to tracking users across multiple sites for proper signal without randomization.
Yeah but if it's opt-in for privacy concerned users there may well be two users in the world with identical basic metadata (browser version, platform, etc) who have this enabled. And telling you it was one of two users but not which is pretty shite anonymization.
Regardless it's still adding an extra bit of information leaked, so you may as well forge a common value rather than make something new up.
Compare that to tracking users across multiple sites for proper signal without randomization.