I have a minifridge too, and a couple weeks ago I was looking for examples of refrigerator mods on the net. Surprisingly I found zero, although I always hear about these kinds of mods at LAN parties and whatnot...
I think it's possible, but you just would have to have some way to actively dehumidify the air in the fridge, otherwise everything would get soaked by condensation and then destroyed.
If you were using the refrigerator to cool the water for a regular water cooler setup, that would probably be a little easier to deal with. You would have to take the same precautions as with a peltier setup (like greasing the pins, applying silicone to the parts of the board that get cold, foam insulation around waterblock and processor), but you would have the advantage of not having to worry about peltier failure. I would suggest however, having the heat exchanger in the loop after leaving the waterblock and before entering the reservoir in the fridge for best cooling performance.
As to the watercooling system in the "home brewed water cooling" article, I would suggest something other than senfu.