I checked Snopes, which has a long list of Coke rumors, but this wasn’t on it.
Here’s what I heard: Computer analysis has been able to break down “secret recipes” that heretofore were… well, secret. One can therefore buy a knockoff of an expensive perfume for 5 bucks at your local mini-mart. It seems these computer analysts turned their machines and expertisde to Coca-Cola. And found the “secret ingredient” that no one has been able to replicate all these years is… a derivative of tobacco ash.
This page has a recipe along with a bunch of other stuff not related to your question, but as far as I can tell, no tobacco products.
In fact, my 2:45 am google-fu reveals nothing pertinent to coca-cola and tabacco ash. And I can’t taste any tobacco ash in the diet coke I’m drinking now either. But since it’s diet coke, I can’t be sure.
When they removed traces of cocaine, I doubt they decided to leave traces of burnt tobacco. The chemicals involved might be similar, but I can’t imagine that such an ingredient would even be considered.
Note that it only cliams that Coke contains a product that is “a derivative of tobacco ash”. That is almost certainly true, the same way that dynamite is made with peanuts. The “truth” lies in stating that the substance is a derivative of tobacco ash without actually saying that the stuff in coke is derived from tobacco ash. Lots of things are derivatives of tobacco ash, including water. That doesn’t mean that Coke actually contains material extracted from tobacco ash.
The most common derivative of tobacco ash would be sodium carbonate and potassium carbonate. Not exactly an unusual components of a carbonated confectionary drink.
Also keep in mind that recreating the taste of Coke (or any soft drink) is trivially easy. But the strength of the product is the image and marketing, so there’s little or no benefit of producing that product.