I have had some experience in the bottled water business so think I can answer your question. No, water does not "spoil" per se. But I think you are asking the wrong question. It should be "After extended storage, will this water (as you have described) be safe to drink?"
The answer to that question is "Yes, if you have taken care to store it properly". Water can become contaminated from both organic and inorganic sources. Since you have boiled the water, it should not have any source for organic growth in it. But what about the container. Was it sterilized, too? If not, that could be a problem (especially if it previously contained a sugar based liquid). Also, how was it sealed? Is it airtight? If not, that could be a possible source of contamination. Also, it should not be stored in sunlight, which promotes organic growth as well as deterioration of plastic. A problem would be evidenced by organic growth in the water.
The other possible problem is that molecules from a plastic container will leach into the water over time. Nothing you can do about that. The good news is that this is primarily a taste issue (the water will taste bad). I doubt you will be drinking enough of it to make it a health issue. The rate of leaching is dependent on the type of plastic. You described "2 liter Coke bottles". These use a fairly soft plastic with a relatively high leach rate. Depending on the environment, these types of bottles are also prone to deteriorate and leak. They really are not suitable for long term storage.
The best medium for long term storage is glass (which is why you can still drink 50 year old wine). Glass is easily broken, however, as well as being heavy. A good compromise would be a polycarbonate plastic bottle. Polycarbonate is a high quality, relatively hard (and thus expensive) plastic. It is used for making car bumpers and eyeglasses, for example. The larger the bottle, the better, as that maximizes the amount of water for the surface area of the plastic. The bottled water industry uses both 3 and 5 gallon polycarbonate bottles, and those are what I would recommend to you for your storage.