In very rare cases, the water pump impeller will become disengaged from the pump shaft and the only way to determine this condition is to remove the pump. Most water pumps have a «weep» hole in the pump casting, and if coolant is leaking from that hole, the pump definitely should be replaced.
If the bearing is extremely worn, there will be noise and looseness of the pump drive pulley which can be detected by applying sideways force on the pulley. A leaking water pump is usually the result of a worn out pump shaft bearing which will cause the seal to leak. If the leak is significant, you will soon notice coolant dripping on the floor and in severe cases the coolant will even spray from the point of the leak. This test should be performed without the engine running. It is important not to exceed the normal operating pressure of the cooling system which is usually marked on the pressure cap. The pump will have a pressure gage attached. The best method of determining a coolant leak, is to pressurize the cooling system with a hand operated pump which is attached to where the pressure cap is removed. A defective thermostat will cause the engine to overheat within a few minutes from a cold start. A defective thermostat is the most common cause of engine overheating but this condition will not necessarily cause a coolant leak unless the engine is operated beyond the maximum operating temperature which will force coolant past the pressure cap and out the overflow hose or tube. If the engine is over-heating it is usually a result of low coolant level which could be caused by a leaking hose, gasket, radiator or the water pump.
Before attempting to replace a water pump, make sure that the pump is the cause of your problem. There are a lot of mis-conceptions regarding water pump replacement.