would the scratch be possible in Calliborn's session, since he technically is a time player? I mean he clearly had some sort of planet on which his quest bed was on when he died, so could there be something there to scratch?

The scratch is caused by sending the Time player’s scratch construct to Skaia and switching the meteors from the Reckoning. Since Skaia blew up in his session and there was no meteors to switch I doubt a scratch is possible in his session.