Will my water pump leak if it's not working on my 2001 Toyota Avalon?

Before changing anymore stuff, first confirm that your radiator cooling fans are coming on at the right time. If not, check fan fuse, fan relay, coolant temp sensor and fan motor. Concerning water pumps: if they are turning, they are pumping. However, there are cases of water pumps with plastic impellers deteriorating so it won't pump. Can't tell without removing it but first, try to look down into the radiator for movement/flow of coolant while revving the engine while hot. That would indicate if it's pumping.