How much 'gain' would we get if we sunk a 55 gallon barrel into the relatively cool ground here in Florida, filled it with calcium free water, and sprayed the condenser in a closed loop cycle when it is running?
Any evaporated water would be made up with condensate.
My system already does that with the condensate. It needs to be kept clean to avoid legionella, and will improve efficiency slightly in a dry atmosphere where it will give a cooling effect. How much improvement it would give I can only guess.
I've worked in more than one data centre where on the hottest day of the year, a few people have had to stand outside spraying the condensor units with hoses, and it makes an enormous difference.
I'm less certain in your case though. You will eventually warm up the 55 gallons of water which will significantly impair its cooling ability. Also you will be spraying this heated water into the air. You could end up infecting someone in the neighbourhood with legionares disease. This is one of the most common ways it breeds and is spread.
Just trickle that down the the condensors as it's produced (or find some way to atomize it and blow it in -- some condensing boilers in the UK do that to get rid of the condensate with the flue gases, but I've not seen how they do it). Don't store the water at all. There are a number of portable air conditioners which do that in the UK, and although it helps with the efficiency, reducing or eliminating emptying of the condensate tank is the main motivation.
I don't think it's necessary in an air conditioner which isn't storing or recyling warm water.
I had a friend (now retired) who looked after the local parks and fountains. It was an ongoing problem finding something they could use in the fountains which prevented bacteria and algae, was non-toxic when someone decided to drink the water from the fountain, and didn't produce large amounts of foam.
The compressor (when integral with the motor) is cooled by the refrigerent going through it, and therefore expects to be hot. A fan blowing at the compressor won't do anything significant (maybe a few tens of watts at best, when the thing is generating several kW anyway). The heat from the compressor is carried away by the refrigerent and dumped in the condensor, together with the heat extracted from the evaporator.
If the radiator is hot it will be cooled by a spray whatever the humidity.
It's going to be a drain on the natural water cycle though, except that in Florida the natural water cycle on humid days supplies large volumes of slightly nitrogenous preciptation.
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