You can monitor it, but is it encrypted? Voice at the quality the Echo records can be compressed down a lot. The Echo has enough processing power to filter data (as in, throw out boring data / near silence) and compress the good stuff. It can send the payload out whenever it wants.
As far as I know, no one has done useful testing. You'd have to run an Echo for some large window of time (30 days?) in an environment with lots of talking without the hotword (Alexa or whatever) and compare to an environment without much talking. Then you'd need to compare the amount of data sent out and try to correlate it with the amount of data it should be sending out based on the use of "Alexa" and the control/baseline environment unit.
Further, you're assuming it only uses your network. It could use any cell band without you knowing it, and with no obvious antenna or other hardware.
And what if the Echo only starts spying on you in excess when triggered by Amazon or some criteria (e.g., the Echo hears you say "Trump")? Your network monitoring only tells you how much data has gone out, ti doesn't tell you how much data could be sent out in the future or what the data contains.
In this day and age, do you really trust a corporation to respect your privacy?
Do you really trust an always-on, internet-connected microphone to not be spying on you?