To a certain extent. You don't have to make sure you're catching and accounting for 100% of every possible data point that might be collected by a browser if you're randomizing everything else though. Random value + consistent individual value will always produce a changed hash.
If you randomize everything that sounds like a pretty identifiable signal tbh. Unless a very large number of people are also performing that randomization. A large number of people specifically in whichever discriminating group you belong to, which might be something out of your control.
Fair enough, it may be more reliable against general/naive approaches like commercial uses though a sufficiently skilled adversary may only consider the fingerprinting techniques they have missed (one specifically targeting TB users).
