I don't think it fundamentally changes the volume of air to be delivered to the engine, or more correctly, the swirl flaps by opening and closing don't in themselves act as the limiting factor in delivering air into the engine.
At low air (flow) requirement (low load/revs), the air is moving slowly, and so the closed (partially closed) flaps help to introduction turbulence to that slow moving air to improve fuel-air mixing before combustion. At higher revs/air flow speed, the air is naturally more turbulent and the flaps open so that they don't impede air delivery to the engine. The speed and and therefore inherent turbulence with the faster moving air results in optimum fuel-air mixing.
This is why when doing the 'resistor mod' to electronically 'delete' the swirl flap motor, you disconnect the arm to the flaps and fix it in the open position (because if it was left in the closed position, the closed flaps could become the limiting factor in delivering sufficient air to the engine under high air demand conditions).
*I think