K.M. Richards
Program Director, The Eighties Channel™
At least some of them would. The 1961 doo-wop song "Those Oldies but Goodies (Remind Me of You)", which popularized the term "Oldies", wasn't singing about rock'n'roll, which by then was only a few years old. It was singing about the big band and crooner music of the '30s and '40s.
The real question would be "how many of the listeners back then made that connection?" I suspect few or none, and that still wouldn't have made Tommy Dorsey acceptable as a Gold spin in 1961 on a top-40 station.