Back in the days before VCR's were common in homes, my cousin would often use a basic tape recorder to record the audio from an episode or movie of TOS as it played to listen to later. I think it worked quite well. Leonard Nimoy even makes the same observation in I Am Spock when talking about the difference between Star Trek and Mission: Impossible; namely that the former could be understood listening from the next room while the latter required you pay attention to the visuals.
The visuals in TOS were important, of course, but you can eliminate them and still understand what's going on from just the audio.