I'm not a hundred percent sure about US washing machines (you guys still use 50s vintage technology top loaders, right? wink ) but european machines use centrifugal pumps in which a plastic impeller spins in a housing with quite a lot of clearance. They can run dry pretty much indefinitely, as they usually have a fan mounted on the other end of the motor shaft to cool the coil. I'd be surprised if the US machines don't have a similar pump, in which case you should be fine.

pca
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Experience is what you get just after it would have helped...