The problem is that it's going to require about 40 pounds of ice for a 5 gallon batch and unless you work somewhere with an industrial icemaker, it's not going to be cheap. You'll want to be stirring the icewater the whole time you are draining.
Bobby_M is correct, and since ice usually isnt free, how do you figure how much ice you need? The easy way is, figure 8 lbs if ice per gallon of wort to get from 212f to 70f or less, this is very close. Another way is, ice takes 144 btus of heat input to melt, then 1 btu per pound to raise the temp each 1 degree F. One gallon of water weights 8.33 lbs, so to cool 5 gallons of wort it (roughly) takes: 5 gallons x 8.33 x1.040 (the average sg of your wort) x (T1-T2) (the current temp minus the desired temp) x sh (specific heat, 1 for water) of heat output from the wort, to get it cooled to yeast pitching temp. The specific heat of sugar water is probly gonna be different than water, which is 1, but the basic equation works the same. Still have to get the sg in, because btus needed is in pounds, gotta convert gallons of wort to lbs. Anyway, figure your wort at 212, you want it to 70 to pitch yeast, this is 142 temp difference. Say, 5x8.33x1.040x1x142=6150.9 Btu to get rid of. In theory, once all the ice was melted, you would have 32 water in your chiller, and 70 wort. This means you could get away with a bit less than 40 lbs ice. Ice at 32 has 144 btu per pound, plus another 38 btu that will be used when the water raises temp from 32 to 70. The amount of ice to get a lb of wort from 212 to 70 would be 6150.9/(142+38), about 34 lbs. Factor in inefficiencies, ice melting from heat absorbed from atmosphere or vessel walls, faster cooling when the coolant and wort temps are further apart, or if you want your pitching temp less than 70, and about 8 lbs ice per gallon works pretty well. Also, ice comes in 8 lb bags around here usually.
Copper vs plastic: with copper it would be alot faster than with plastic because copper has alot better thermal conductivity. Plastic would eventually work, but with its lower ability to transfer heat, it would take alot longer, if lengths were the same. You could use way longer tubing, but it could become a hassle. Copper also has a lower specific heat than plastic, about .09, so it takes less heat from the wort to raise the temp of the copper, to transfer to the ice, than it does from plastic, with a sh from .2 to .6 ish, depending on what the plastic is. Also, the thickness of the coil tubing is a factor as well. Copper being thinner is another plus. If you want it fast and are willing to spend money on 40lbs of ice, I would suggest also spending money on a copper coil.