This situation is why I continue to keep a receiver between a TV and the things connected to it, even when the receiver's gonna be hooked up to absolute shitboxen of speakers I picked up at the thrift store for a dollar each. Being able to turn off the TV without disrupting the audio is a godsend. Nowadays receivers have HDMI inputs, too (on top of the gazillion other inputs available on a typical receiver), so it's entirely unnecessary to ever do anything on the TV except turn it on or off and it's absolutely wonderful.
Don't many TVs communicate bidirectionally with receivers now? When I turn off my TV, my receiver turns off as well. Which is usually what I want. If I want to only use the receiver, I can connect my laptop of phone to the receiver directly via bluetooth. No need to involve the TV.
Yep. Should be labeled CEC unless the TV's UI hides that behind "user friendly" naming. I also have mine set to turn on/off the AV receiver with the TV, but it can be disabled. Only drawback is that you then need to remember to turn off the receiver.
Though the device on the other end may not cooperate, like if it's playing something that uses HDCP it might stop playing when there's no display on the other end of the connection to handshake with. No idea if this is a problem with an Apple TV though.
They can't just totally do it, at least: then the last hop to the actual display would be decrypted, sort of ruining the whole point of HDCP. My understanding is more that a receiver is just a passthrough for the communication between the source and the display. Though I'm surely oversimplifying.
The receiver could always reencrypt (and usually does, IIUC; signaling this is the point of the "repeater bit" in the protocol). If it was just a dumb passthrough, then there wouldn't be much need to advertise HDCP compatibility in the first place.