A follow-up post so I can address the actual question...
I've never attempted audio-only with any Trek except TOS, and that was a matter of technological necessity. Any conclusions I might come to will be semi-educated guesses.
I could be a smartass and say TAS could be a purely audio thing, since the visuals weren't worth keeping one's eyes open in any case.
It's likely that the other Treks would mirror my experiences with TOS - some episodes would work pretty well and others would be useless as pure audio. Just to pin myself down, I'll say ENT seems like it would hold up in audio better than the others.
It would be Ok as long as you fast-forward the opening credits.
I'm curious to know why you think ENT would hold better than the others? If I were to pick a series that I can imagine holding well on audio, ENT would hardly be the first to come to mind.
Generally, Trek series could hold on audio much better than the movies, which are far more action-oriented and visual. I'm guessing that TNG might hold well on audio since it was quite "talky". DS9 would hold very well except for the episodes that had a lot of action or space battle scenes; but there are quite a few episodes like "Duet" that are based on dialogue and character interaction, that I can imagine working very well on audio. You would lose the advantage of seeing the emotions on character's faces, but most of them acted very well with their voices, too.