Can a script read from a character's turn order value?

Hm?

Yes, see wiki . In short, use JSON.parse(Campaign().get('turnorder')); to get the current data from the turn order (note: make sure you check whether the turn order is an empty string first), and use Campaign().set('turnorder', JSON.stringify(myTurorderData)); to set the data. The linked wiki page has an example of inserting a "Turn Counter" item to the order set to a value of 15.

My apologies, I actually meant in a macro, not a script. Duh.

Macros? No.

No, but you could create a script which could then be called from a macro.

Ah, interesting.