How do FaceTime and Push Notifications work on wifi-only iOS devices?
For what it's worth, my iPod Touches' (2g and 3g) WiFi remains on when the screen is off, and I do get push notifications from various things (in fact, as I was typing this I got one from Ambiance).  If you go out of range of known networks and "Ask to join networks" is turned on in the WiFi settings, you of course won't get push notifications unless you turn the screen on and accept an open network.  The Apple battery life optimization page has a little more information, including how to control on a per-application basis what push notifications will work.