Not in the ‘60s they didn’t. The Sting came out in 1973. But something like the Maple Leaf Rag was always known.
There were vestiges of 1920s music in popular entertainment in part because Ed Sullivan gave air time to old vaudeville acts.
Then there were the variety shows (sometimes hosted by former vaudeville performers like Jack Benny or George Burns, in addition to song and dance numbers of shows like Laugh-In).