I have seen water pump impellers eroded to barely a stub on the end of the shaft, a condition hastened by infrequent coolant changes. So the only circulation of coolant is by thermosiphon (convection). Before WWI and even up until the early '30s engines often circulated coolant by this principle, aided in part by a significant area of the radiator located above the highest point of the water jackets in the engine. Modern high compression, high performance engines with low set radiators rely on a properly functioning water pump.