This should be possible. The AirPort does not require an Internet connection to work. By default, it will broadcast an unsecured wireless network with a Network Name of something like: Apple Network NNNNNN. Both your Apple TV and your iPad should be able to connect to this network to allow AirPlay Mirroring from the iPad to the Apple TV.
Ok so we now have a solution to the problem. A friend of mine came round to work this out with me last night and we were able to get it working, but it is not as easy as I had hoped. Fisrtly we plugged the airport express into my router using the ethernet cable (for this I am using an Airport Express Base Station") and in airport utilities selected the airport express. In edit, we then gave the airport express a new range of IP address which did not conflict with any of the other applications that I have already assigned. We also named the Airport Express with a distinguishable name. We then waited for the changes to be registered then unplugged the Airport Express from the router. I then plugged my AppleTV via HDMI into a tv to test it and selected the new wifi network with the new Airport Express distinguishable name. I was able to watch a video that I have on my ipad directly on my tv without being connected to the internet, and was able to play Airplay presentations.
No the easiest solution, and certainly not something that anyone at Apple has talked me through in my lengthy conversations with them at Applecare.
Hope this helps.