Yes and no.
The pump isn't pumping air directly (unless you are low on coolant). What is happening is that the pump is spinning so fast that the low pressure side of the impeller gets so low that the coolant actually flash boils (boiling temp goes down with pressure drop) locally, creating air bubbles that then collapse. That collapse is cavitation. The real problem with cavitation is that it leads to increased wear on the impeller blades, and also a lose in pumping efficiency.
Another thing to consider, is that just because you increase the pump shaft velocity, it does not necessarily mean you will be pumping more fluid. Every pump has an efficiency curve based on many factors, like the blade design, inlet restrictions, outlet restrictions, Net Positive Head, etc. If you spin the pump too fast, the impeller will move out of it's efficient zone and all that will happen is you will increase the power demand of the pump, increase the heat generated in the pump, and increase it's wear and tear, all while losing efficiency and likely not increasing fluid flow significantly.
But then again, I'm not a fan of reworking water pumps on engines. If the car is running warm, look for the cause, not a bandaid. Flushing the system, new hoses, new radiator (or recore), etc. Even timing and engine tune effect the cooling system.