Airplay, wi-fi and related questions before purchasing an Apple TV
Hello. using airplay shouldn't generate any traffic at all to the external network as it is only local. You should count in though, that while cellular data is turned on, your phone probably accesses it (all the services like push, location services, update checks etc) go out there to download information. If you connect your apple tv to your phone, the tv accesses the web as well. I am not shure of how much traffic is generated, but I am afraid you can't stay at 0 with this configuration.