I can't see any reason that a work comprising primarily of white noise couldn't be copyrighted.

What you can't do is stop others copying your idea (as long as they don't copy your implementation), nor stop others implementing the same thing who don't copy you.

Now, a work needs in most jurisdictions to be distinctive, but IMO the length of the work would inter alia be enough to make it distinctive, or perhaps use of a specially designed noise generator. But when you release "10 hours of noise" and I copy your idea and make "9 hours of noise" there will be no tort there.