Been thinking about this. You could achieve the functionality by adding an apple tv and a small wireless router. With the iPhone 5 the AppRadio no longer actually "knows" that the phone is plugged into the radio. It just knows that something is plugged into its HDMI port and that your iPhone is linked to it via bluetooth. If you used an apple tv as your piggyback and then had a very low power wireless router to give a connection to both devices it would actually be perfectly possible to do what you want.
Only problems I see is that
1. there will be lag on touch response.
2. You will run into a problem with the apple tv and router boot time which would be horrendous, or
3. if you don't want that problem you have to find a way to keep both the router and the apple tv on at all times without draining your battery.
4. At home of all places I've had issues where my apple tv randomly decides that it doesn't feel like working because it just doesn't. A little annoying at home. Would be utterly infuriating in the car.
However, yes this should work.