It does sound somewhat nefarious. I can say some gamers like to hear the sound of their own voices through the headphones when they are playing...of course usually in that situation the headphone mic is being used, not the phone mic!I don't know if there's an app, there probably is because it's a simple audio pass through, but they don't do this by default.
Why do you want this? I can't think of a use for it that isn't super sketchy lol.