I tried with my iPhone 4S and iPad Mini Retina earlier today, and these are my findings:
iPhone 4S stacked to Hugo's back worked fine. If I moved the iPhone just a little bit away from the Hugo the noise got back.
It seems to vary a little bit. If I set music at pause the noise is not that bad (some times), but if I started playing from the source the noise got worse.
So in my findings the noise do vary a bit.
And to my findings the noise do not vary with volume. You can more easily hear it with volume all the way down.
The noise was heard using the Beyerdynamic T5P with Moon Audio Black Dragon V2 cable.
I tried my Sennheiser HD800's too with the same cable and I could not hear any noise at all, even when placing my phone a couple of meters away.
With the iPad Mini Retina I had to place the Hugo on top of the iPad's front glass and on the bottom half to get the noise away.
Same experience with my headphones.. the noise was heard using the Beyerdynamic T5P with Moon Audio Black Dragon V2 cable, and not with my Sennheiser HD800's with the same cable.
I never really enjoyed the "Bluetooth sound" though (with or without the noise).. but as you (Chord) have stated before.. you will need aptx support to get the best out of the Bluetooth connection, and unfortunately for me iDevices don't support it. Luckily for me I have an USB cable and a camera adapter that I can use, and that sound I do love!