You mean the man in the grip of the exotic fever they injected into him while he apparently was unconscious after the beam-down? Between his illness, whatever extra drugs he was given, and Odona, Kirk wouldn't be particularly attentive.
Kirk wasn't injected with an "exotic fever", nor is there any indication that he was injected with anything at all. He was unconscious for 9 minutes while they took a blood sample from him. As for rendering him unconscious in the first place, drugs aren't the only way to do it, especially in the Star Trek universe (a phaser on stun or a single magical "karate chop" to the back, neck, or shoulder seem to be the easiest ways). Furthermore, there is nothing to indicate that he was given any drugs, and there is their admitted medical ineptitude (because they have no need for medicine) to suggest that they didn't.
In any event, this episode was absurd for more than one reason. For one thing, the Enterprise mockup wasn't even needed for their plan (which makes it a colossal waste of time/resources, even if we pretend it is plausible for them to have built it in the first place). They could have beamed Kirk to a small locked room with the girl already in there and have accomplished the same thing. In fact, it probably would have accomplished it faster, given the heightened sense of danger of being in a small locked room as compared to simply wondering where everyone went on your huge ship. It is well known that people tend to bond quickly in dangerous situations.
For another thing, they hoped Kirk would fall in love with the girl and thus want to stay because of her. However, the plan for her was to die in short order. So what did they think the incentive for Kirk to stay would be once she was dead?
And of course, the idea that they could have built a mockup perfect enough to fool someone who has been on the Enterprise practically 24/7 for the past 3 years is quite a reach. The only way they could do that is if they had "replicator" type technology, which can scan the Enterprise on a molecular level and perfectly recreate it on a molecular level.
A mere optical scanning process of the interior surfaces (pretending for a moment that they somehow had enough access to the Enterprise to do such a thing) wouldn't provide nearly enough information to create a copy which would fool someone who is intimately familiar with the original. To give one of many possible examples, the foam in the captain's chair wouldn't feel right, because it wouldn't be broken in in the same way as the original, and there wouldn't even be any way for them to make sure the foam was even to the same manufacturing specifications as the original (not that that would help much, because the original is no longer new, and thus feels different than new). Plus, a lot of things were functional, and optical scanning can't tell you how the internal electronics/mechanisms are designed, and if you were to just wing it, you'd inevitably only end up with an approximation, which couldn't be expected to fool Kirk.
I have several NES controllers, and even though they are all the same make and model (Nintendo Controller Model No. : NES-004), they all have a different feel to the D-pad, which means I have a preference for some of them over others, and a
strong preference for one of them in particular. On top of that, they have different levels of wear and tear (scratches, scuffs, dings). I even have a pair of NOS (new old stock) ones that I've only used long enough to test functionality, and their D-pads feel different from each other too. That's just the inherent nature of the manufacturing process, i.e., it is impossible to make two items which are truly identical without sci-fi molecular-level replication technology.
