Putting the coil of tubing in a pot of water in the fridge increases the thermal transfer dramatically . I kept a 55 insulated on 3 sides at 60 degrees year round. Weather you need it for a reef is up to the OP. I can turn the ceiling fan on high and keep mine at 79 when it's pretty hot. If he's just wanting to drop it a few degrees the fridge will do that.OK, I'll be the one to say it point blank...it won't work.
Plastic tubing, air interface, heat transfer, flow rate. You couldn't pack enough plastic tubing in that frig to make a difference.
It's been tried with chilled water and efficiency is so poor, it won't work.
Throw an inexpensive window air conditioner in your fish room and sit back and have a cold beer!