Water pumps are rarely responsible for overheating, except on some Volkswagens.
Anything that is leaking will result in a low coolant level, and eventually it will stop circulating. That will cause overheating. Also, if the level is low enough to expose the thermostat, it won't open, and that will aggravate the overheating. Thermostats open in response to hot liquid, not hot air.
Before you go looking for a problem that may not even exist, solve the leak, then see if the engine still overheats.