No you couldn't. Coca Cola itself actually only produces unsweetened syrup which is what contains the "original formula". From there it's up to the canning/bottling companies to decide what they want to use to sweeten it, within reason. Coke does actually own most of the bottlers it uses in some way, but they're treated more as a separate company with actual internal competition and such. Bottlers still have to buy the syrup from coke to produce the product and then pay for their own sweetener, bottling, etc cost. Coke still pays for advertising though.
In short... ignorance on how this product is made lead to silly ideas.