They do mention the unused main title theme. McCarthy says that from the get go they were gonna do the Goldsmith's TMP, and after they did sessions on that, he was asked to try to make an opening theme this time without Goldsmith's music. I think the unused theme was likely just something they wanted to have around in case the producers decided not to go with Goldsmith's theme. Either way, it's now dubbed as "the Picard Theme" which the host Jeff Bond mentions.
The Picard Theme is something McCarthy only used every once in awhile, usually for a heroic moment for Picard or a grand Enterprise moment. I don't think he ever used it again past the third season. I found some examples in YouTube.
Here's the cue used again in "The Child" at 0:30.
Here's the cue being used in "Yesterday's Enterprise", twice during 1:39 and 4:10.
There are plenty of other moments I could cite. Like in "Sins of the Father" when Worf asks Picard to become his Cha'DIch. What I find most interesting is the fact that Ron Jones is the only TNG composer to actually use the Goldsmith theme within the episode. McCarthy never did that (there is the saucer seperation sequence, but that was tracked music from the end credits, here's the music he actually scored for that sequence at 0:41 http://www.youtube.com/watch?v=yP6D4V1_b4k
). I think it's too bad Jeff Bond never asked McCarthy or Chattaway why they didn't use the Goldsmith theme during episodes. On the liner notes for the box set of Ron Jones music, it's explained that he used the TMP theme a lot during the first season, but by the second season he started to no longer use it. By the third season, he only used the Courage fanfare twice as he wanted to continue making brand new music for the TNG crew now that they were starting to step out of TNG's shadow. I think this is a good example of him deciding to make new flyby music instead of relying on either Goldsmith or Courage fanfare at 52 seconds in: http://www.youtube.com/watch?v=YxklAsl2v2I