My biggest issue with a progress bar would be how to quantify it into numbers. I don't know what half complete would be, because the work can vary so easily. We could come up with some arbitrary markers - finished reading it, judging action, scoring, etc - but those would be difficult to mark on the bar given every judge's different process.
Judges PMing writers, especially for full judgments, sounds like a much more sound idea. It wouldn't create the same amount of pressure as a progress bar and it would help put a face to the writing their reading, perhaps motivating them to further push it along without the same amount of stress. And, of course, it shows some availability to communicate between community and staff, and that's always a good thing, before and after judgement, in case any questions arise.