In most cases it's a bad idea to add fine organic matter to your run, as it will make the run muddier/muckier/swampier as time goes on. (In contrast to large organic matter like straw or big wood chips, that can -- and in most cases should -- be raked out and replaced before they have decomposed too much). If your run is on extremely free-draining nearly pure sand, or something like that; or if it is clayey but on a real 'height of land' and never has mud or puddle problems; only then would it be ok to be having shavings in the run long-term.
If your pophole is cut at floor level, such that adding a respectable height of sill would make it too short for the chickens to easily fit through, you might want to get out the saw and cut it taller, so it maintains its height when a sill is added. I actually prefer 12" or so of sill between the top of the shavings and the pophole bottom; mine have no trouble whatsoever hopping up and over/through, and it keeps essentially ALL the bedding in the coop, no matter how deep and no matter what the wind. They do have a 6" flat area (my walls are 6" thick) in the doorway; if your pophole is just cut through thin plywood, it would be a good idea to screw a piece of 2x4 flush with the top of the plywood on whichever side won't interfere with the operation of the door, so they essentially have a flat 2" 'perch' to hop onto in the doorway there instead of the thin edge of the plywood. (Which they would still use, btw)
Good luck, have fun,
Pat