I think it is a great idea and I see no reason why it would not work just fine. That is how they cool the water through the door on big fridges--they have large coils of tubing hidden somewhere in the fridge. I think that a 1/2" ID line is going to be too large to cool effectively if the water is moving. I would go with either a 3/8 or 1/2" OD, although I do not believe that a 1/4" line is too small. Depending on the size line you get, you may want more than 100'. The most effective cooling will come with the most pipe in the fridge. Get the thinnest wall diameter possible as the water is not going to be under any pressure (to speak of). If you have anything large enough to clog the line (even a 1/4"), it is going to clog the pump before it clogs the lines--the lines will take a small amount of debris, the pump won't.
I'm with you on using polyethylene lines rather than copper, even if prices were the same--there is a large chance that the nutes reacting with the metal in the copper.