Cliffhangers, outside of soap operas, don't seem to exist prior to 1978 (Soap, which itself was a parody of soap operas). The cliffhanger was popularized by Dallas in 1980 (Who Shot J.R.?) purely because Larry Hagman was haggling over a raise - and that ballooned into one of the most popular television episodes of all time. Dallas, it should be noted, was also very soap opera-esque.
So, Star Trek would have to be practically inventing the cliffhanger (as it applies to primetime television dramas) to use it in 1969. Presumably due to a behind-the-scenes commotion with one of the regulars (Shatner or Nimoy, but probably not Kelley). That's not out of the question, with Roddenberry already gone, I'm not sure what drama occurred at the end of the season and how it jibes with contracts.
My guess is that the episode would be almost entirely self-contained, with the cliffhanger coming out of the blue (a Klingon agent stabs Spock! Kirk is transported off the bridge!). This way, they could edit out the cliffhanger for syndication.
If the show is cancelled, the cliffhanger ending will be largely unknown (outside of fan circles) until its re-release in some Star Trek special airing in the late '80s, and there'll be some question to its canonicity for awhile, as the movies never address it. Plenty of novels and RPGs reference the event, and there may be even a joke in the reboot series.
If the show is somehow not cancelled, then the cliffhanger would perhaps not be cut for syndication (at least some of the time), as it keeps viewers tuned in for the next episode. Although it would have nothing to do with the decision, the cliffhanger may be held up as the reason Star Trek wasn't cancelled (especially if it is even a fraction as popular as Who Shot J.R.?). TOS may get five or six seasons, all ending on cliffhangers (and perhaps more two-parters, although that's pushing it at this early stage). Cliffhangers become popular 11 years early, and some of your favorite 1970s shows will use the gimmick.
