You want as many of those balls exposed to air as possible. Unfortunately, using this to hold a skimmer will force you to keep about 10" of water in it at all times. A skimmer is not going to function properly with a constantly changing water level so i would suggest an ATO as being a mandatory component for this set up.
Those bio balls host aerobic bacteria. the more oxygen they get, the better they work. This is why water is trickled over them, constantly keeping them wet, but not submerged. hence the name -trickle filter or wet/dry.