Having had direct experience with indoor use of this type of air conditioner, I can attest to the impracticality of attempting to cool the hot air in the manner you suggest.
If you had the ability to construct a tower, say 2 meters high, 0.5 meters in diameter, with layers of ice within, but held on open racks to enable considerable airflow, the output of the air conditioner may be cooled sufficiently. Of course, the ice will melt and have to be replaced frequently.
A rough guess here, but expect that 10 bags of ice, US standard 8 to ten pounds may last a couple of hours at the cooling rate needed. That converts to 10 to 12 gallons of water melted by the output of the air conditioner.
You would get insufficient cooling from smaller amounts of ice and most certainly insufficient cooling from water, unless you could fashion a method to vaporize the water to relinquish yet more energy. Unfortunately, the vaporized water would have to be ejected outside, or the room in question would become unbearably humid.
I have a gut feeling that my numbers are on the low side, but if the tower provides good circulation, it might be possible. The logistics of installing the ice and having a sufficient supply is a serious challenge as well.