At least for the 360 they do.
Was singing a song online in challenge mode with a guitarist and bassist. I asked him if he could hear me while I sung (I could hear an echo of myself coming from the headset) he gave me a yes.
I turned off the headset and sung with just the microphone so I couldn't hear him if he was saying anything. After song was over, he told me that I was still heard.
Dunno if this applies to the Quickplay mode. Or if its just my settings that make em hear me.
Anyone having same problem?