No so sure, there is a ping that is performed by the box towards openpli.org and also towards google.com but I don't know which process and why the boxes are doing this.
But except a ping they should not have bandwidth consumption except if you decide to port forward to access your box from the internet and some smart people are using you box against your will.
That ping only happens in the network setup, to verify if your settings are correct. It pings an IP and two DNS names to verify IP and DNS connectivity. Similarly, if you choose to update or flash an image, network activity happens.
What I meant was that there is NO process in OpenPLi that requires network activity, there is nothing running in the background that requires it, that constantly checks something, etc. No "Phone Home" feature in the code either.