it would work for the fan maybe, Its just a 110V AC motor just like in a drill press...
A swamp cooler adds moisture to air that is way too dry to cool, Like in the desert. It puts a mist (dampness) into the air and blows it out vents and such, A regular air conditioner doesn't cool the air
if its too dry and would cost alot in electicity to run compared to a swamp cooler
I have never lived on Mars nor in a desert.
The air conditioner in my home reduces the humidity and cools very well. Its electricity cost is low because it is high efficiency and electricity is cheap here.
Swamp coolers (https://en.wikipedia.org/wiki/Evaporative_cooler) are a very economical method of cooling the air in low humidity parts of the world...outside of Canada. Think if the old wool blanket covered canteens people would hang on the outside of their cars on trips...for free water chilling.
If you mean the washing machines water pump then yes it wprobably would work, depending on the amount of water you want to shift.
The only watch out point is that washer pumps are designed for intermittant use not continuous.