Getting rid of conscious thought processes is not specific to playing by ear - it also happens if someone learns a piece by heart, and it happens for good sight readers, who can turn visual patterns of notes into finger movements without conscious thought.
Playing by ear is turning sounds into finger movements.
Playing from notes is turning pictures into finger movements.
In either case, the beginner has to use conscious thought processes and the expert doesn't have to.
And in either case, it is possible to learn a piece, so that the external stimulus is no longer required.