I've had it both ways, Last night i was streaming netflix through my Blu-ray player and i had it only while content was playing. Once paused it went away.
A couple days ago I noticed it with nothing playing (first caught my attention while streaming music), turned the volume up to about -10 and it was quite noisy, went to access the sound menu in startup and the noise went away as soon as i opened that menu.
I miss-described it, more of a constant rushing wind noise then true white noise. Kinda like you would hear on old vinyl records or tape recordings.
Forgot to mention it may not just be audyssey, it goes away when receiver is set to pure or direct modes, but theater its there and with audyssey on its the loudest.