Not a chance. Having to pass through the skull (which wouldn't be too difficult as you are cutting through a joint at the top of the skull, and the facial part would shatter), the cervical vertebrae (which again you may achieve, as they are relatively small and weak). The katana would most likely be stopped by the sternum (breast bone) and thoracic vertebrae and stop somewhere around that point, if that.
There is no chance in hell that you would be able to cleave all 26 individual bones of the spinal column (especially since the spaces between each would mean an impact after each vertebra, which would mean you could get less far than if it were a sinle long bone), the skull and the sternum in one stroke