Yes, technically, but they don't have sufficent cooling capacity. What you can do is run a metal waterpipe through the refrigerator's coolant loops with a slow flowrate pump. Then just cool the CPU or something. Or you could just go water cooling, drill a hole in the fridge, stuff a radiator in the fridge, seal the hole with clay...
I believe the fridge with the radiator inside would have sufficent cooling capacity to cool an AthlonXP 1700+ or an AthlonXP 1800+, keep it at around 40C.
I wouldn't suggest trying to cool everything with a refrigerator, you'll overload it. Open up your powersupply, (Be careful, and after you disconnect the power press the power switch to make sure the capicators are drained) take out old fan, put in vantec silencer, cool the AthlonXP with passive cooling from the radiator in fridge (You can stuff the resivour and pump in the fridge too and just use a water block outside the fridge)
A word of advice, if you go with radiator in fridge approach, put it in the bottom of the fridge, as heat rises.