Hey,
I'm with the FacePlant team and I'd love to answer some of your questions. The app doesn't require any user intervention after you've completed the initial setup. You give us your phone number and a name, the app launches and syncs up your contacts, and then that's it. We use iOS 4's backgrounding and some special tech we've written to do the rest.
As for private WiFi networks.. the app doesn't care about that. As long as it detects that you are connected to a WiFi network and have internet access (same as you would need to make a FaceTime call), we consider you "online".
If there's anything else I can help answer, don't hesitate to e-mail us -
facetime@rallyapp.com
Thanks!