You wont be able to leave the coil in there for any length of time because any beer in the lines will freeze.
If you want you can make a couple of "jockey boxes" by buying some copper tubing, coiling it in a 3-5 gallon bucket and fill it with water put it in your freezer and when solid hook it up to the keg. Or make a real jockey box and keep ice on hand all the time. OR buy, borrow, steal a kegerator.
just my $.02