Not really. TMP makes it pretty clear that it's about two and a half years after the end of the 5-year mission, while TWOK is explicitly 15 years after "Space Seed," so there can't be fewer than about 8 years between them, and the currently accepted interval is 12 years (because the Okudachron inexplicably put TWOK 18 years after "Space Seed"). So it works out to about a decade between them plus or minus 20%. There's some uncertainty, but not enough to allow for placing them close together.
I think that's the what I was half-remembering; I knew there was something about the fifteen-year figure that was at odds with other concepts.
Granted, some fans (and novelists) did interpret TMP as taking place in real time, about a decade after TOS, by presuming a second 5-year mission between them, or just an extended mission of unspecified length. That interpretation would've put TMP & TWOK fairly close together, maybe as little as 3 years. But that required ignoring Kirk's line in TMP about "my five years out there," which pegs the intended interval pretty explicitly (and was the first canonical mention of the 5-year mission in actual dialogue as opposed to main-title narration). So I count that interpretation as an error rather than a valid alternative view of the timing.
Yeah, that's been an old idea (the
Lost Years TOS novels way back when, the original Chronology slotting a spot for the canceled
Phase II series, etc.) Also been an idea in some stuff that the TV show only covered the first three years and that there's two years missing, instead of the official position that TOS/TAS are spread out across five years instead of one year per season/cartoon series.
Correct me if I'm wrong, though, but, as I recall, looking at things pretty closely, it's "just" assumptions on the TMP dating. Yes, Kirk mentions spending five years in space, that he hasn't gone back in 2 1/2 years, that the refit was eighteen months, all stuff that would date the movie as 2 1/2 years after the end of TOS (now TOS/TAS, with the cartoon now being canon again), with the exact year being 2273, per the 2270 end time of the TOS/TAS mission.
However, all that assumes that all those things started right after the mission ended, which, as I recall, is never confirmed. We're just told that these events happened x number of years before the movie, not how they relate to the TV show. Even the Okuda chronology, based on these data points that started it all, in the second edition, made it clear that it was just a theory, not fact as of the time of writing. (Not to mention that all the official reference material still use the old 2271 year, despite that being based on the now-debunked conjecture that the mission ended in 2269 and this being known for some time now.)