Not if the random part of the list changes with each request.
There are two ways to defeat fingerprinting: 1) make everyone look exactly the same (pretty difficult to do), or 2) introduce enough noise and randomness to fingerprinting signals to each request so that each person looks like many different people (much easier to do).
Comments
This is an easier fingerprint signal than just not sending anything.
Not if the random part of the list changes with each request.
There are two ways to defeat fingerprinting: 1) make everyone look exactly the same (pretty difficult to do), or 2) introduce enough noise and randomness to fingerprinting signals to each request so that each person looks like many different people (much easier to do).