I think what you are asking for. Always able to use voice even when the phone is off is something that's part of the hardware. I was told this by a friend who works for Sony Erricsson. it's something to do with the phone going into a psuedo 'sleep state' but still having certain functions in the hardware work and not drain the battery as it would if the phone was on. He did admit that having that on a MS phone with Cortana would be pretty awesome, but Microsoft would need to implement it inside the hardware like specific droid phones do.
hope that helps you out
Not necessarily. What you describe was implemented in the Moto X and that remains the only mainstream phone to have true always-listening capabilities. The OP here has a different phone which can do active listening only when plugged in (so that the battery doesn't get drained). The Moto X however is always listening whether it's plugged in or not, and it has a special low-power voice recognition chip to do this.