Mine is always there when the radio is on. Turn off the radio and it goes away completely. If I am on a call with the bluetooth with radio off it returns. And interesting enough if the radio is off, not on the bluetooth, and turn either turn signal on it will return. If I want silence while driving I need to turn off the radio, not answer the phone, or use my turns signals; what a wonderful product chevy has given me.
With that info it's clear to me that the sound is generated only when the amplifier has to be used, i.e.: radio, phone, signals. All of those require the amp to be powered for the sound to be generated.
Like SS has asked before, and which you have answered, no matter the volume when the radio or BT are in use, and no matter any other load, the sound is a constant dB level and pitch. It would seem that the amp itself is generating the noise, either through the speakers or from one or more components it is built from.
My '09 and this '11 both have a similar noise from under the hood when the key is in ACC or RUN. It's not audible inside, but can be heard with the hood up or down. There's an electronics package between the battery and the radiator support that the noise comes from. It makes me think it is something like a power transistor or IC that is being cycled somewhere around 12-20,000 times a second, and the power running through it is such that the switching/cycling is audible.
I would hazard a guess that your amp is having the same issue. To me it just screams cheap stuff. I've never heard any other car do this, ever. And to have it coming from more than one component suggests to me that GM contracted with a manufacturer to supply certain parts to meet certain criteria, but either that criteria didn't include audible noises or they chose not to worry about what they've discovered.
Since my noises are coming from under the hood and don't bother me while operating the car I'm not gonna do anything unless there's some kind of recall or TSB. I hope they find the source of your noise and get it corrected before it drives you completely nuts!