no the ice machine will keep it cool. Most models are for under the counter, available in 15 and 18 inches. (I used to work for an appliance store)
The water line must be attched, and must have a drain also. The way it works is the water is distributed down a small plate inside and ice begins to develop on the plate, when the plate gets thick enough is drops onto a wire grip that heats up and cuts it into cubes. they are very popular because the ice tastes very fresh and there are no chemicals or elements in the ice to make it taste weird.
(this is why when you pour coke into a glass of normal ice it fizzes. Its actually the deposits in the ice that react with the co2)
Coke wont fiz with this ice. They are a little expensive, but worth it if you use a lot of ice, and drink lots of coke
You should expect to pay anywhere from 500-1500 bucks depending on the brand and size. My top choice, Kitchenaid. Sub-zeros are too expensive. check scratch and dent and you may find one cheaper. they come in black, stainless, or white. It saddens me that i know all this crap...
They do make a portable one that makes ice on the counter, but its like 400 bucks, and appeared to be a total waste of money to me. I saw it for sale in one of those "skymall" magazines on an airplane.