I'm pretty sure Alexa isn't recording or transmitting what's said at all times, there's just a local process looking for the queue to start recording a sample to upload. That queue being the word "Alexa".
Oh, I think the proper word was cue, not queue, by the way.
Maybe? Maybe you'd be comfortable? There's a world where you wrote the code yourself and still don't trust that it's not sending data back?