By banning the box, those individuals would at least have the chance to get their foot in the door. Background checks would still be performed on the candidates, but not until after they have already made an impression on those hiring.
In Rex Huppke's column in the Chicago Tribune, he does a great job laying out why banning the box is good, but more is needed. By taking more pro-active steps to help rehabilitated people get employment, we can reduce recidivism and get talented people into positions which need them. Society is helped twice over. Illinois lawmakers have recognized this fact, and have begun implementing some steps. President Obama's executive order will hopefully serve to extend this understanding to the national stage.