A:Answer Joe,
No, the Audio Out will only carry the audio signal. You'll need to connect the included USB cable to the transmitter and a power source in order to charge the transmitter. Most new TV sets have at least one USB port on the back that can be used to power this type of device, but if yours doesn't, or if you're already using that port to power something else, you'll need to supply a USB charger like the one I've attached to this answer to provide power to the transmitter.
-Brendan