Oh, that it were true. According to the Aggies over at Prairie View A&M, the chance of killing the ants by drenching the mound with club soda is "slim to none." It is founded on a fact, however; club soda (in large quantities) can kill lots of organisms. But fire ants build mounds 12-15 feet underground and even further horizontally. It would take more club soda than the local bar dispenses to reach that far. There is one bit of good news, though. A club soda drench very well might make the ant colony move, since they don't like to be disturbed. Hey, if they want to pack up and move down the road, I'll happily supply the luggage. - but I'm keeping the Campari.
You can find an explanation of the theory and its debunking at the blog Insects in the City, under "Club soda for your ants, Sir?"