If using an auto-switching HDMI switch, and if I have my Sky box as one input and a disc player as another, and the Sky box is currently powered up and I'm watching that, when I turn on the disc player will the auto switch give me the disc player even though the Sky box is still powered up?

I ask since Sky boxes take forever to boot and the last thing I'd want to be doing is turning it off and on simply to de-power the output so the auto switch can give me the disc player input.

Anyone enlighten me as to their experiences?