I'm wondering if you're not overthinking this. Copper is a great conductor, but with all the bends and T junctions that thing is going to be impossible to clean. And you're going to have to do that eventually. Otherwise that copper is going to oxidoze and collect all kinds of weird flavors.
I'm just not seeing how it would do any better than a three foot section of plastic tubing coiled inside a cooler full of icewater.