It's been impossible for me to reconcile the cop numbers, but I think there's no doubt:
From the very beginning, Mayor Nagin and Police Chief Compass were attempting to cover up NOPD corruption.
With their exaggerated stories of cop heroism, exaggerated stories of New Orleans violence, death, destruction, murder and mayhem. I think the Las Vegas/Atlanta R&Rs for cops was a part of it too.
Maybe some cops did desert, the following article gives a number. We don't know how many of that number were the phantom cops or actual deserters.
http://www.lasvegassun.com/sunbin/stories/nat-gen/2005/sep/28/092801085.html