It can be done. In another game I'm in there are 3 mods who handle everything including apps. App cycle is the 1st-10th and all apps are processed by the 12th at the latest.

These mods all work or go to school full time so it isn't a matter of them sitting around doing nothing all day. And while occasionally a bad app does get in, for the most part they do a pretty fucking good job of being on top of things.