It vaguely strikes a bell. Of course all phones back then contained a cheap carbon microphone - called IIRC the 'mouth piece'. It would always be a working 'microphone', only cut off by the hang up switch.
My memory ain't good enough to remember how to work around the hang up switch - but agencies like the See Eye Aye long had ways of working that sort of thing out - maybe even the NYPD techs❗