Yes it would, To receive the OTA update you do need service on your phone. Also note since you state it is rooted it probably has CWM or TWRP as it's recovery. Even with data the update will fail. The phone would need to be taken back to Stock unrooted and Stock recovery. Once this is done you my try connecting to your PC via USB and see if Kies will update the phone. Again it will need to be stock unrooted.