TrekCore's screencap gallery for the episode:
Kirk and Seven (and Isis) are in the same shot for much of the first transporter-room scene. In the long shots, including the fight sequence, we see Gary in the same shot with Kirk, Spock, Scott, and two guards. We also see a 3-shot of Gary in the foreground with Spock and Scott in the background. (Screencap pages 5ff)
Later, in Gary's office (pages 22-23), we see Roberta in the same shot with Kirk and Spock as she tries to stop them from going in. They get into a scuffle, so there's definitely direct interaction between them.
In the climactic scene (pages 43ff), first we see Kirk and Spock in the shot with Gary, but Gary has his back to the camera so I can't be certain it's Lansing. But we then cut to a 3-shot of Gary, Roberta, and Kirk. Later there's a brief 3-shot of Kirk, Spock, and Gary, then we intercut between a shot of Roberta and Kirk and a shot of Gary and Spock, and yes, there is briefly a 4-shot of all of them standing in front of the Beta 5 (p. 45).
Also, there's that call sheet in the Discovered Documents page linked to earlier. It shows that Shatner, Nimoy, Lansing, and Garr all worked on that same single day of shooting, and on the same sets, Gary's outer office and library.
So no, this isn't like "The Menagerie." It's not two things shot at different times and then cut together. It's just the opposite -- one thing shot all at once but designed so that parts of it could be cut out later.