I actually saw a Monte Carlo well over a decade ago that someone was using as a daily driver and from which they'd removed both the radiator and the water pump. And they claimed that at the time I saw it, it'd been running for over a year that way.
Edit: I've had cars in my youth that'd freeze up from not having enough antifreeze. One was a Datsun 510. It'd start but the belt would screech something fierce until the water pump would finally start turning and it wouldn't idle until then, but once the water pump broke free, everything would be just fine.
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