Primitive two stage evaporative cooling

Compared to single stage evaporative coolers, two stage coolers are more efficient, but the added stage takes up considerable space and is costly to manufacture. For this reason, two stage coolers (in the USA) are mainly seen in industrial settings and evaporative coolers for residences are only single stage coolers.

Would it be possible to get some of the benefits from two stage cooling cheaply by having a fan that blows air across the outside of a single stage cooler? This would help cool the pads of the cooler due to evaporation, and some of the air blown by the fan would not be pulled into the cooler, so its humidity and absorbed heat would not be added to air sent into the house.