Can a bad water pump cause antifreeze to seep into the engine oil?

No, a bad water pump itself doesn't directly cause antifreeze to seep into the engine oil. While a failing water pump *can* contribute to a situation where this happens, it's not the direct cause. The problem lies in the *cause* of the water pump failure, or a related component.

A failing water pump might lead to overheating, which could crack the engine block or head gasket. It's the cracked block, head gasket, or a damaged cylinder head that allows coolant (antifreeze) to mix with engine oil. The water pump's failure is just an indirect contributor by leading to the overheating that causes the more serious damage.