Luckily it's possible to check [0]! Although it gets a bit more complicated and can change, my understanding is that currently most people observe it increase it's network usage after it's trigger phrase, but not at other times (it uses the network for other stuff too, but audio data is typically rather large in comparison).
[0] https://www.iot-tests.org/2017/06/careless-whisper-does-amaz...
[1] 10.1007/s00779-018-1174-x <- Might want to use sci-hub