Does AirPlay online stream to Apple TV still go through the iPad? When we AirPlay the online stream on iPad to Apple TV, does the iPad remain in the chain (online stream to iPad and then iPad to Apple TV) or does the Apple TV virtually get and play that stream (online stream to Apple TV)?
If you stream a video from the internet, and then AirPlay is to a suitable receiver like an Apple TV, then all the devices in the chain still take part.  The Apple TV doesn't simply get the stream location and other data like playback location, then stream it by itself, it get's a secondary copy that the iPad is essentially repeating onwards.

You can easily test this by streaming something, then airplaying it to the AppleTV, then turning airplane mode on the iPad - the Apple TV stream should fail.