Just using water to transfer the heat into the refrigerator, rather than putting the computer in there, won't solve the problem(same number of watts being exhausted). However, you could set up a two stage system if you are feeling enthusiastic. Something like the following: Coolant is pumped through the waterblock(s), picks up heat, moves to a fan cooled radiator, drops back to just a few degrees above ambient, then passes through a refrigeration system, drops well below ambient, and flows back to the waterblock(s). This would, in theory, allow you to get sub-ambient cooling(beware the dew point, as above mentioned) without having to buy a refrigerator that can pass several hundred watts continuously. Even if the refrigerator dies, you'll only have ordinary water cooling. You might have a much easier time(and a more portable system) by just having a peltier or two in your coolant basin. Something like
http://www.goldmine-elec-products.com/p...mber=G14582&variation=&aitem=2&mitem=3 embedded in the wall of the coolant tank, with the cold side fully exposed to coolant flow, and warm side fan cooled, will get the sub-ambient coolant effect without the entire minifridge.
Of course, once you bring watercooling into the picture(as you basically have to) you really start to wonder if it is worth it. A properly designed watercooling system already owns all but the craziest air cooling systems, without the considerable nuisances that sub-ambient cooling introduces(condensation, uneven thermal expansion, etc). Also, every sub-ambient cooling system is less than perfectly efficient. It will release all the heat generated by your system, plus some extra that they generate themselves. Your core will be cooler; but your room will actually be hotter(unless you bleed the heat directly outside). So, unless you just want to do it because it is a hardcore mod, or you happen to be really, really cranking your core speeds and voltages, don't bother with anything above watercooling.