Now this obviously doesn't rule out the device saving stuff locally, but plenty of people have verified that it does generally only send lots of data to the server when you have just asked it to wake up.
Not saying that they do though since if they were discovered to be doing that, it's way too damaging for Amazon's reputation for it to be worth going through the trouble.
For example, you could root the device and disable the encryption.
Or, you could perform experiments in a controlled setting where you play a series of identical recordings to Alexa and measure the statistical similarity in the outgoing data for each. The encryption scheme probably provides more entropy than just the audio, so maybe statistical analysis wouldn't help, but it's a start.