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".
I believe you're right, but it still feels icky to have something always listening for that special phrase, to me. Maybe if I wrote and maintained the code myself that always listened, I'd feel more comfortable with it.
Oh, I think the proper word was cue, not queue, by the way.
You could try adding in some simple motion, like raising your hand, before the system would start listening for hot words. Maybe connect a cheap infrared sensor to GPIO and block its view so it only detects motion at or above certain height.
Oh, I think the proper word was cue, not queue, by the way.