"The Cage"(cut from 63 mins. down to about 44)was part of the basic syndication package in my area for years before Sci-Fi got the rights to the series in 1998.
Yeah, a shorter version of "The Cage" was added to syndication package quite a while ago, before the series went to Sci-Fi. So the answer to the original question is that "The Cage" has been shown on TV many, many times, though for the most part it was the truncated version.
I haven't seen any updated schedules but it seems the TOS-R version of "The Cage" will be shown before the new movie opens. They seem to be on a countdown, with TOS episode #3 (The Corbomite Maneuver) airing this weekend followed by episode #2 (Where No Man Has Gone Before) next weekend. So "The Cage" is probably after that, airing the first weekend in May.