I can see a way to use dry ice in an RDWC system; drop it in the control bucket and let it help chill the nutrient solution while the CO² vapor gets blown around the room and utilized by the plants.
How expensive is dry ice? CO² is about $8 for a twenty pound refill. How much does twenty pounds of dry ice go for? How much is all that cooling worth, while we're at it?
FWIW, it's going to slightly carbonate the water while chilling the Fuck out of it. My admittedly uneducated guess is the resulting pH jump will do more harm than good.