I think a regular air-conditioner would draw more electricity than freezing/chilling some water, then passing this through a fan.
Regular A/C's draw into the kW's of electricity - although smaller systems would be around 500-800w of electricity.
So I fail to see how a regular system would be 'cheaper,' when the fan and compressor will pull easily 10x more power.
Such a system that produce condensate like this would work very well in hotter climates where the heat is DRY not MOIST - due to the evaporative cooling effect. I imagine the air produced would also be several degrees cooler than the room air.
If one had all these accessories sitting around, not doing anything useful, I think this would be a worthwhile project for cooler, dryer weather. Sweltering heat needs refrigeration, not swamp/evaporative cooling anyhow.
(i.e. On a 104° day, an evaporative system can only take it down to about 86° - an improvement, but certainly not when you factor in the "sticky" factor with that. )