Given that none of the TOS episodes ever referenced Starfleet Command HQ in terms of something they passed over showing then, no. It was never something they ever even considered showing.
I took the communication with Admiral Fitzpatrick in “The Trouble With Tribbles” as possibly going back to Earth. Just by virtue of the importance of the project and Fitzpatrick’s rank. He was the only full admiral they ever showed.
There was certainly a lot of talk about what it might have been, related to Phase II. Much more than what ended up in TMP. And very much in conflict with later depictions. Here is how Roddenberry describes it in his TMP novelization, should you choose to attempt it-
“Whatever one prefers to call it—Starfleet Command, Fleet Headquarters, or the Admiralty—it is centered in a structure which
thrusts itself magnificently spaceward out of the redwood forest of San Francisco’s old city peninsula. Although some museum cities have taller buildings preserved from the industrial past, Starfleet’s headquarters are still a
distinctive landmark in this world where so much of the clutter of our lives has been placed underground.
“Just under two hours ago, Kirk had taken the tube from Gibraltar to Los Angeles Island, where he had caught the first northbound airtram. Now, fifteen minutes later, the clear blue waters of San Francisco Bay were in full view. As always, the sight of Starfleet’s headquarters seemed to make Kirk’s heart beat a bit faster. Since his midshipman days, he had always admired the
clean symmetry of the design and its dramatic combination of space and Earth materials. There was an almost
storybook castle suggestion in the way its
tritanium-blue superstructure rose up out of its gray-granite base. It had always been to Kirk a statement in architectural poetry about a very necessary relationship between the mud below and the stars above.”
I did my interpretation of this for my unfinished 50th anniversary manual. I’d love to see your take.
