Can you still run the engine without overheating when water pump timing belt is broken?

No, you cannot reliably run an engine without overheating if the water pump timing belt is broken. The water pump is driven by the timing belt (or, less commonly, a separate belt). If the belt breaks, the water pump stops circulating coolant. This will lead to rapid overheating and potential catastrophic engine damage within a very short time – minutes, at most.