I think the most that anyone could do would be to identify the ingredients used, and even that would be difficult without knowing exactly what you were looking for. Being able to say exactly what the ratios of the various ingredients would be impossible I think. There are many companies trying to produce drinks as close to Coca Cola as they can but they've not managed to get it exact.
I can't see why a "scientist" would want fo do as you suggest: if they did manage to identify "the secret formula" then surely they'd try to sell it to the highest bidder. The whole deal would be clandestine.
You can't copyright or patent a recipe though - it's like if you watched a baker making bread there's nothing anyone can do to stop you from going home and duplicating it. Obviously no one could call it "Coca Cola" and rules in some countries might even stop anyone even refering to the brand. I believe there used to be rules in some countries that provented anyone saying, for example, that a drink was as good as, or better than, or more popular than, or just like any other specific drink.