As long as we talk about blueshirts doing command jobs, let's remember Captain Robau from this very movie...
(Or should we perhaps argue that the three colors are rotated every once in a while in the UFP Starfleet, so that the command color is gold in TOS but red in TNG and blue in the 2230s, thus explaining why both Robau and George Kirk wear blue?)
When the no-win scenario test was introduced in ST2, it was made clear that it was optional and (at least for Saavik) postgraduate, and that it had been a fixture of Starfleet training for at least the past few decades. TNG was the first show to deal with the issue of Starfleet (undergraduate) training, when Wesley applied for the Academy; he was shown confronting such make-believe scenarios in his entry exams already, supporting the idea that Starfleet still believes in this sort of testing/training in the 24th century. But Wesley never reached the circumstances where Kirk or Saavik took their respective no-win scenario tests. DS9 gave us Nog, who did graduate, but again (AFAWK) without reaching the Kirk or Saavik phase because he was expedited through the training to supply the front lines of a major war.
STXI, then, is really the first instance of Trek returning to the themes of ST2. That the test is optional is again supported: McCoy isn't taking it. It would be weird to put him in the center seat once he has already acted as "supporting extra" to Kirk's test. That the test is postgraduate is not supported - but if it's optional, one may argue that one indeed only takes it when aiming for command, and some (like Kirk and nuKirk) know their aimpoint during undergraduate training already while others (like Saavik) only decide later on.
So, did nuSpock take the test or not? Based on the above, there's no telling. It really is optional, one can return to it later on, and it mutates over time (indeed, perhaps only the specific variant designed by nuSpock involves a ship named Kobayashi Maru, and Kirk in ST2 picked that one for nostalgic reasons). As the point of the test is not passing vs. failing, but rather wading through and learning, nuSpock could easily have taken it and "lost" without feeling dissatisfied with the result - thus leaving Kirk as the first one to "win".
Timo Saloniemi