I just checked the autostarts app on my Android phone and it does seem as waze is set to auto start when connectivity is changed.
The info for the 'connectivity changed' status states that "The current network connection has changed, for example: when switching from wi-fi to GSM. Note that since this is also triggered when a connection is initially established, it effectively entails the 'On Startup' behavior."
So the "What is it doing in the background?" question is valid and I would like to know as well.
...when you care enough to Waze the very best