You are removing bacteria, fish waste, any polutants is the air that settle into your tank, you are adding o2 to close to saturation levels, you are gettin rid of co2 gas in your tank. Like brad said the coral slime will build up in your tank and rot making more poison. Skimming is the way to go. JMHO. steve
Skimmers remove proteins and other organic compounds from the aquarium before they have a chance to break down and foul the water. These organics are brought up a cylinder chamber through micronic bubbles cleaning their surface.
You live in a walk-in closet - The closet has a vending machine that is stocked with food for you, and you have a bar fridge full of beverages.
Unfortunately your walk-in does not have a private restroom... In fact not even a hole in the floor.
Now after how many days, hours or minutes... are you going to be asking (if not begging) someone to bring you a nice Hepa Air Filter ? Or even open an air vent.
While your system may handle a variety of filtration needs given your filtration, live rock, and sand bed. Still creating a good gas exchange, as well as pulling out those organics that build up are big benefits of skimming.
PS - I will not be putting together a comparison test of who can live in a closet the longest.