To be fair, it only needs to cover the phone's average power draw if you put in a supercapacitor or small conventional battery.
But there's another problem.... if I understand how this works correctly, for a 1W battery, the radioactive element must be outputting AT LEAST 1W of radiation energy at all times, whether it's being consumed as electricity or not. Ideally that's all trapped inside as heat in a best case scenario, but having to cool your battery while it's not in use is kind of a deal breaker for anything more than milliwatts (or it will have to have a heatsink as big as the battery)