I am certain the answer is no. According to a letter to the editor published in Variety in 1937, Brooks appeared on the radio in the mid-1920, most likely in 1926 while she was still a resident of NYC. (It's possible she appeared on the radio in 1927, or even 1928, as she was known to criss-cross the country during that time.)
I feel claims of E.M. Orowitz can be believed. In the past, I have found radio listings and newspaper articles which corroborate his claim. One article I came across, for example, stated that while the Louise Brooks film, A Social Celebrity, was playing at the Rivoli in New York in April, 1926, Adolphe Menjou appeared on WGBS, the Gimbel Brothers radio station in NYC. According to this newspaper report, Menjou spoke about the film and the scenes shot locally on Long Island.
This is a significant discovery, at least in terms of Louise Brooks biography. Should there be any surviving records, documents or even (unlikely) recordings, then its significance grows.