That's the strangest thing I have heard all day.
It's a physical impossibility - you can only video record a broadcast dot.
It isn't original. I knicked it from "The Young Ones" but I could see where the scriptwriters were coming from.
As an undergraduate there was nothing after the late night film and national anthem and white dot. There were times when we'd have happily watched the dot and listed to the whine because we were incapable of movement and were grateful for any form of stimulus reception that confirmed we were still alive.
As young parents, TV sourced stimulation during the night shift had evolved to "The Hit Man and Her" with Pete Waterman and Michaela Strachan followed by the eighty or ninety page carousel of Teletext/Ceefax Jobfinder. Both of which provided, by a very small margin, more stimulation than the white dot and whine. I don't recall every hearing the National Anthem at any stage through the night.
So I reckon sometime before 1988 was when the anthem went walkabout.