i doubt that would work...
that metal coil wont be able to cool the air any less than ambient temp.. which is still usually too hot..
you dont really want to have your nutrient water running through a metal hose, unless that metal is stainless steel, which is not very bendable.... i think titanium might also be safe, as that is what they use in chillers.. other metals will screw things up and poison your plants...
i tried so much stuff - i've tried running a coil of hose into a mini-fridge, i've torn apart a mini-fridge and put the cold coils (which usually make up the little "freezer" part) in the reservoir... i've broken the hot side of a mini-fridge after i got it torn apart, and had to braze a schrader valve onto the compressor and braze the hot side back together so i could refill the compressor with refrigerant... i've gone through enough mini-fridges to pay for a good chiller... but ultimitely changed to a system that was less dependent on reservoir temperatures. Still dont have a good chiller...