2001 Oldsmobile Intrigue serpentine belt and water pump

I brought the car to a mechanic they replace the serpentine belt and the water pump. My question is does the serpentine belt have to be on the water pump to turn it to work properly. Prior to bringing the car in I was not experiencing any overheating problems like I am now. So I looked at the engine and notice the serpentine belt was not on the water pump.