Someone has a similar idea about using cold water for cooling here. I recommend checking those responses.
Wouldn't doing this cause the temps of the crapper water to get hotter as usage drags on and therefore start to show diminishing returns?
The thing that makes standard water cooling so effective is that there is a constant stream of air running over the fins of the radiator, but what you're trying to suggest would put the radiator in a pool of water that has no cycling for heat and in return would slowly start to creep up in temps.
I might be thinking of this wrong but think of the example of a car radiator. Coolant goes in is blown on by a fan and the ambient air flowing over the radiator and fan while the car moves but as soon as the car stops moving temps start rising as one factor of cooling is subtracted. And this is with the pump still running.
You're suggesting a stagnant pool of water to cool something that is constantly putting out heat. There will be a time when the heat will start to raise temperatures to a point where this setup would not be any better than a fan and rad loop. Doesn't seem like the best idea.