Chilling a kettle in a fridge would take a long time (I can't give a number without knowing more, but I would guess hours) because air contact isn't a very efficient method for cooling a bulk liquid.
After your wort gets cool enough that the ground water isn't doing much, you can run ice water through your immersion chiller rather than using an ice bath. My kettle is too large for my sink, so I can't use an ice bath. Instead, I have an immersible pump (for water fountains, etc) in a small picnic cooler that pumps water through the immersion chiller. I run tap water into the cooler at first, then begin adding ice later. When the return water gets cool enough I put the return water back into the cooler to make a closed system. This will take roughly the same amount of ice as an ice bath but will cool the wort faster, and it is a lot easier because you don't have to move the kettle.