I still say that has nothing to do with it, because they were not "the crew." They were Academy cadets assigned to the ship for a single training flight. Basically it was a field trip. Their experience or the political situation had nothing to do with it; they were just never meant to be aboard the ship for longer than that one training mission. And the training cruise was a birthday outing for Admiral Kirk, which suggests that it was intended to be just a day long. So getting diverted to Regula I and getting their butts kicked by Khan made them all very, very late for their next classes.
It was definitely going to be more than a day or two. Kirk says he's glad to have Sulu at the helm "for three weeks," and the infamous trimmed line after that makes it clear he's phrasing it that way because that's when Sulu leaves to take his new job, and not because the training cruise will be done. The cadets' on-board practical experience could've been planned to be their classes for an entire quarter or semester.
Of course, we also don't know how much of the training cruise was finished. The plot doesn't synchronize until Marcus calls Kirk. That could've been anything up to three weeks after they left Earth, if only because Sulu hadn't slipped away yet. The only clue we've got is that it's a short enough people of time that Saavik hadn't had a chance to speak to Kirk privately off-the-record about the Kobayashi Maru, but considering he's the Admiral on a ship with hundreds of people, they could just have not crossed paths in any sort of semi-private space before she caught him in the elevator.