The water pump is driven by the timing chai so I would think not. Am I missing something?
Well your alternator is driven by the serpentine belt and you a/c, fuel pump and most radiator fans are electric. I don’t know if you would get far enough for the car to overheat because of the lack of electricity to the cooling fans.
I might be able to give you a better answer if you had told us what prompted the question and what make,year, and model are.