It's a constant volume noise, so yes, present with music, and audible. With the cheap chinese DAC that I mentioned the noise is the same, but quiter, music masks it. Which is odd because DX1 uses a boost converter, I would expect it to have much better PSRR. Maybe it's the DAC stage that's noisy (I don't know whether or not it's fed by the boost converter, I just assume it's not).
DX1 has some sort of stand-by mute that removes the noise after a couple seconds of input not being active. Since it can cut the noise off, this is another indication that it's the DAC stage and not the amp stage. This also means that the amp stage is exceptionally well isolated.
Or, it just cuts power to the headphone amp and then the above is not true.