No, I do not believe most native speakers of at least US English would understand the phrase "light a rag." It is argot, jargon of the underworld. But The Sting was peppered with argot.
David Maurer, who was a professor of linguistics specializing in slang, jargon, and argot at the time, provides in The Big Con the definition of this phrase, and other terms of argot, particularly those pertaining to confidence games, as they were used in 1940, when his book was published.
Quite a few terms pertaining to grift that were used in The Sting are defined in this book, and the big-con game of "The Wire" was portrayed in the movie pretty much as it appeared in the book. So was the small-con game of "The Switch" shown at the beginning of the movie.
Some other terms from the movie explained in the book: "Up and Down Broadway," "blew him off/blow off," "braced game," "kayducer," "cold deck," "told him the tale," "boost," "quill," "boodle," "shut-out," and, of course, "sting" (which has since been corrupted in "sucker" (non-grifter) language, making it a "sucker word"). These are the ones I can think of off the top of my head; I'd wager there are more.
The book also covered the ruse in which Gondorff appears to shoot Hooker (the "Cackle-Bladder"), and the use of FBI agent Pogue to help chill the mark ("The Button"). In fact, the book frequently mentions a Charles Gondorff as a prominent inside man. Another name mentioned in the film, this one exactly as it appeared in the book, is "Limehouse Chappie."
The finger-to-nose signal J. J. gives the other members of the gang is one of several called an "office," though this particular gesture has a different meaning when described in the book. We also see that saloon-keeper Duke Boudreau is a local "fixer," and may surmise that Kid Twist has that moniker because he is a lady's man.
If you were to read the book and then watch the movie, I think you would be amazed at how many of the phrases, scenarios, and actions are described in Maurer's book.
In summary, The Sting contains many phrases that are specific to grift and cons and are not understood by most native speakers; "light a rag" is only one of several.