I don't know if independent noise can do the trick. I would guess it still has to be somehow correlated to music, or focused at least. maybe only on bass to make for some "texture" ^_^ .
but the idea that the cleanest sound isn't the best sounding music, I very much believe that. at least as long as we listen to crap masters I'm sure of it. some stuff sound great in a car, but when I get them in my headphone I cry. I've been disappointed a good number of times like that.
Deviation from the input signal correlated to the input signal is distortion, not noise. The SNR addresses a different facet of playback, and I wouldn't want to mix variables if I ever got the chance to try this. The point is not to find a pleasing sound sig or to trick people into thinking they hear tubes by introducing even order/inter-modulation distortion into a clean signal (though I think that would be a fascinating experiment on its own too) but rather to explore what SNR people really need for enjoyment.
It's worth noting that these super high SNR ratios (110db+) are not found in any natural environment with a natural acoustic source. Classical symphonies have a typical dynamic range 50-60db, with a fairly high ambient noise floor due to the audience. I won't get into rock concerts because those can be artificially amped into hearing damage levels, and an electric guitar is not a completely acoustic instrument... but even rock concerts (within safe SPL levels) have dynamic range limits well within the range of CD, and also have relatively high ambient noise levels. Let's say a person hypothetically wears isolating headphones that bring the noise floor to 15db, and then listens to an amp with 120dbSNR and HD material with 120db+ of dynamic range, is that a truly realistic depiction of any naturally recorded material? No symphony you ever attend would yield such an experience in either DR or noise floor. The ability to accurately reproduce live music was achieved a long time ago. We've become obsessed with technical numbers that have no correlation to reality anymore, assuming the bigger the numbers the better the experience. It's the musical equivalent to pixel peeping, and does very little good to expose the greater or more realistic picture of what you are looking at.
I bought an assortment of Louis Armstrong records. My CDs of him are often fatiguing, and I think the higher noise levels and limited dynamics of vinyl might actually help. And, after all, those albums and songs were originally distributed on vinyl anyway. I'm curious to see how the experience goes.