Can rigid foam board have an air space between it and the studs. Basement wall
It's fine to have a gap between the rigid insulation and the energy wall IF you don't allow airflow to occur between the gap and your conditioned space. If there's free flow of air from on space to the other, the insulation in your energy wall effectively does nothing as you've now basically placed the insulation in the middle of the room. 

This means relying on your drywall, plus something at the top of the gap, to completely block airflow. For that reason it may prove too complex.