I had a try of this last night for you using an Iphone 5 and Apple TV2 hooked up to a 32" screen. I've also used some, but not all of the catch-up apps with an ATV 3 anda 46" tv in a different room, the reason for the "some" will become apparent.
When it works it works well, if you have decent wi-fi and the catch up itself natively supports airplay then it's a great solution, PQ is good and motion is no problem. The unfortunate thing is that only iPlayer and Demand % support Airpaly natively. For ITV player and 4OD you need to use Airplay mirroring to see anything. ITV Player works fine over mirroring PQ and SQacceptable but not as good with the native apps whilst 4OD has a safeguard which won't let the app stream even via mirroring and a screen comes up stating that the 4OD app does not support conection to a TV.
Last edited by RSK; 01-02-13 at 14:11.