... When a player edits their character, does that lock the database in a way that a GM cannot edit the GM notes
... Will the GM's change be lost?
Your GM notes cannot be touched by the Player and should work for you regardless of what the Player does. In fact, its the other way around… you can lock the Player out of editing their Character.
However, to understand more clearly your situation have you encountered an error while trying to edit a GM box? If so, please let me know what you are experiencing or need.