Re: can "checked out" mean "idling mind" or "preoccupied"
Robert, I believe that "checked off" would be used as an aid to counting/recording; marking a list. So, it would have nothing to do with a preoccupied or idle mind.
"Checking out" of a hotel means to pay for services and leave. Someone who has "checked out" has left the premises. It is sometimes used to refer to someone who is not quite aware of surroundings.
Steve