Im guessing it makes changes in what the apple TV outputs, and doesn't actually make changes with your picture settings on the tv? As from what I understand, the "calibration" is only for content you use the device for, and doesn't carry over.
How does it compensate for the display which has it's own set of adjustments? My projector has a ton of them including gamma curves. The Apple TV box is misconstrued and I think of it more as a tuner not a "TV." My projector is just a display as there is no sound.
Scott, have you got a link for that? According to Alex Lindsay, Apple is making changes to the AppleTV's CLUT (Color Look-Up Table) that takes the desired RGB value for a pixel and does a 3-dimensional transformation so the color output on your screen is a match for the original value. So, it doesn't matter if your TV is set to torch mode (aka Store Demo mode), the tweaked CLUTs should produce a more accurate picture.
And, as long as you don't block the color being sent to the screen during calibration, it should work on a Projector. But without a projector (or an iPhone with FaceID) I can't verify.
I have 10 user settings I can custom set in the projector so I can experiment with one of those. As long as I don't shadow the screen image I don't see why it shouldn't work unless there is a higher NIT requirement. My screen is pretty bright but we always watch in a darkened room. I'll have to give it a try soon.