The answer is NO.
Fire ant control using club soda was recently tested and found to be ineffective.
For a thorough discussion of club soda as a home remedy and how it has been debunked, view the following post from the blog Insects in the City: Club soda for your ants, Sir? and this article from Texas AgriLife Extension.
It is interesting how many so-called fire ant cures have been suggested. Many, but not all, of these have been scientifically tested in replicated university trials. The club soda home remedy, like many others, seems attractive because it is environmentally sound and uses a readily available product. It has a seeming basis in fact, because carbon dioxide in high concentrations is known to be lethal to many organisms. However, the quantity of carbon dioxide generated from a club soda drench would not be sufficient to replace the air in a colony that may extend 12 feet underground. The club soda drench might make the colony move because the fire ants do not like being disturbed.