iphone 3.0 notifications... will it work over WiFi?

Apple unveiled today iPhone OS 3.0. One of the long awaited features was the Notifications API. But will it work over any local area network or it will require Internet connectivity? The beta release only allowed Apple servers to trigger notifications. Apparently the new release has been completely rearchitected. Let's see...

Another interesting feature is the peer-to-peer connectivity. It relies on Bluetooth, not WiFi, so expect a very short range (10m/32ft).