Sure they could, if they wanted to. It wasn't until 1989 that Richard Arnold imposed the arbitrary set of tie-in restrictions that included a ban on TAS elements. It's just that TAS wasn't as widely available back then; it wasn't on home video yet and there were only occasional reruns. So some writers were less familiar with it than others and thus didn't acknowledge it. Or else they were aware of it but didn't believe it counted, not as a matter of imposed restrictions but just as a personal preference.
In one of the early issues of DC's first TOS comic series, there was an item in the letter column where editor Bob Greenberger talked about how he and writer Mike Barr disagreed on whether to include TAS. Bob wanted to include it, but Mike wanted to leave it out. Which presumably is why they didn't add Arex and M'Ress to the comic until Len Wein took over the writing.
But there were some references to TAS in the early novels. Bantam's The Galactic Whirlpool referenced Arex and M'Ress, and the earlier The Starless World referred to the Enterprise having previously visited the center of the galaxy (as in "The Magicks of Megas-tu"). Of course, Howard Weinstein was familiar with TAS since he'd made his professional debut writing for it, and his Pocket novel The Covenant of the Crown reused the disease choriocytosis from "The Pirates of Orion." The Tears of the Singers by future TNG writer Melinda Snodgrass featured Kali from "The Time Trap" as Kor's wife. The Vulcan Academy Murders referenced a lot from "Yesteryear," even though Yesterday's Son had completely ignored it.
Well, her name in TWS is K't'lk. K's't'lk is who she becomes at the end of the book (it's complicated).
The Duane books kind of had to be adjusted to post-TMP, because they apparently were written under the assumption that the gap between TOS and TMP was longer than just a few years, closer to the decade-long gap in real life. There were several books from that era that made the same assumption, that there was a second 5-year mission between TOS and TMP or just that the mission was open-ended despite the title narration. For instance, The Romulan Way is explicitly set 8 years after "The Enterprise Incident," but it's only a year after The Wounded Sky and My Enemy, My Ally. So under modern timeline assumptions, they have to be post-TMP, even though they were written as pre-TMP (Spock's World was the first Duane book to be overtly set after it).
I think Greg was asked by our editor to incorporate the Chekov explanation that I'd given in Ex Machina around the same time (that Chekov had been in engineering and had led the defense against Khan's takeover of that section), although I borrowed mine in turn from Allan Asherman's Who's Who in Star Trek from DC. So Asherman deserves the original credit.
). But retconning some of those earlier novels into a 5 year mission following TMP I think works just fine, and doesn't really contradict the novels since they didn't really come out and say what year it was. Sometimes they'd use Stardates--but we know how malleable stardates were back in the day. In a way it makes everything fit together. 2 1/2 years for the refit, then in the TWOK when they specify it's been 15 years since Space Seed and it all falls together. Plus it means the refit Enterprise was in services for about 12 or 13 years (rather than the just 3 or 4 years if you moved TMP to 8 or 9 years if you add a 2nd 5 year mission to prior to TMP---I mean, who would do a total refit and mothball the ship 3 or 4 years later?).
