this is an awesome idea! my only bit of insight is that the coke is somehow kept below its freezing point in liquid form (which is possible) and when you open it and drink some, you put the ratio of water to air (? maybe, not sure) into a level that cannot sustain liquid form when below the freezing point, so it just flash freezes? anyone? verification?

I think you are on the right track. The coke is kept right near freezing. When you open it up to take a drink you are releasing the carbon dioxide. Once you flip it upside down you release even more. This release lowers the liquid pressure causing the liquid to freeze easier and quicker. The same thing can be done at home by putting it in your freezer for 3-5 hours, at least that is how it is done with a bottle of beer.

oh yeah, and i forgot about nucleation points. ice crystals have to have something to form on, and bubbles make perfect little ice carriers. so you take a swig to lower the level or the drink so it wont spill out and the flipping upside down releases bubbles and forms a ton of nucleation points, that the ice can quickly form on. pretty sweet still.