No. At least in the 1.9.1 version. When you switch from one device to another, the screen contents don't get immediately updated. So you'll see incorrect information displayed for the current Air. Eventually as things like the guiding graph and the images are loaded from the currently attached Air, things get updated. As long as you are aware of this behavior, it's useable. Just don't trust what you see on the screen after a device switch.
I don't know if 2.0 is better.