Literature is the preserved written artifacts of a culture. One of my favorite examples is Moby Dick. Melville wrote within the Nautical Tales genre that was popular in the 19th century. Moby Dick basically examines the entire whaling industry of the day. It was not a hit. But in the early twentieth century, long after he died, the novel caught on. It was a new world. After the inventions of the dynamo and the combustion engine, it was all about oil and electricity. So, you see, the culture that existed for the writing of Moby Dck was almost gone. It was becoming legend. People had distance and could step back and see what written artifacts exemplified this disappearing culture. And that is why Moby Dick changed from being a genre novel into Literature, with a capital L. If you think about ancient Greece you can follow this logic and know why Homer is Literature. It is intrinsic to the culture. Our desire to remember inclines us to cling to these written artifacts.
From my point of view you can not claim that any current writing is Literature, or literary. (I know he said literate, but I am assuming that's a malapropism.) Our culture is still on-going. We do not have the mental distance to stand back and assess the written artifacts of our culture and correctly state which ones deserve to be preserved. We can only guess what future generations will choose.
Also remember that drama is literature, and the drama of our culture will face the same reaper as the novels. The Star Trek franchise includes drama that may or may not be chosen to represent our culture by future generations. It depends on them, really, not on us. The generations in the future of Sappho decided to destroy her work. They burned it in front of the Library of Alexandria. All we have are scraps. That could happen to Trek, too. We do not control that.
But I really hope that future generations decide to keep Trek as they have kept Gilbert & Sullivan or Italian opera. I hope they still have two-dimensional displays and occasionally watch episodes, and I hope they will continue to read and maybe even have Trek Lit courses for an easy A in community colleges. But until they do, none of it is Literature.
Finally, if the original post meant to ask for literary Trek novels, I don't really know if we can agree on a meaning for that phrase. If you set out to write in a literary manner, you will always fail. The only writing that can come of someone trying to be literary is imitation. It's a paradox, too, that you can't intentionally avoid imitation to be "creative". So the good ones write the book they want to read and say to heck with all that jibber-jabber. If that's the question I can only say, thank goodness, no. I don't believe any of the Trek writers set out to be literary. That would be awfully boring.
But if you meant to ask, "Are they well-edited?", the answer is yes. I don't notice many spelling errors or sentences that fall apart. One or two times in a book I will have to re-read a sentence but that's because of the modern American tendency to avoid excessive use of commas. This happens in everything nowadays anyway, so older readers just have to get over wanting more commas. But the editing is fine; these folk are professionals.
That said, the real reason we read these books is because we like the characters and can't get enough of them. If you're looking for literature it's over in 811, in the big room over there.