Nope, which kind of makes the feature much less useful to me.
I was hoping I'd be able to start watching a video on my iPad when I'm preparing dinner and then switch it to the TV when I've finished cooking; but you can't do that unless the video is actually on the iPad 🙁
Hopefully it is just a minor tweak to update Airvideo so it works because currently the only option I get is to stream audio from it (same with BBC iPlayer 🙁, but YouTube & the video app work as expected)
Apple needs to integrate this into the iOS's iPod native app. Where u can play your local content as well as be able to browse and play your computers iTunes library.