As I see it, there are at least a couple of possibilities with all of this:
1) The Apple TV has a 'native' landscape orientation, which means that only when the screen being mirrored is in landscape mode will the full TV screen be filled (and portrait display will only ever fill the height of the screen in landscape mode and there will be black bars on the side of the image for the rest of the screen space). If the TV screen is displayed in portrait mode, the image will be on its side;
2) The Apple TV has a 'native' landscape orientation, but only in regards to the Apple TV menu, which means that as soon as the Airplay functionality is engaged it won't really matter;
3) The Apple TV will accomodate to the orientation of the screen (no matter if it's mounted landscape or portrait, and this will be the case for both the menu and the Airplay mirroring, etc.).
I can live with 2) or 3), but 1) is going to be a real problem.
I don't know if any of this makes sense. Perhaps I'm overthinking it, but the first option is really going to be a problem (so I need to ensure it's not the case).