So, the new Trek movie is rumoured to be an Academy story for Kirk and Spock. This is an idea that goes all the way back to the days when Harve Bennett was still involved with the franchise. It was rejected then, first because the Classic Cast were all still young enough to still play their roles, as long as the story kept moving forward in time; and then because TNG was winding down as a series and Paramount thought that was more fertile ground for movies.
Fandom has often rejected the idea as well, for different reasons, which ultimately boil down to the general sense that it's a dumb idea and something of a cop-out plot.
Many also argue that it's an impossibility, because they assume that Kirk and Spock could not have been at the academy together, but that's specious. Assuming that
Memory Alpha is getting its information from reasonably reliable sources (such as the Star Trek Encyclopaedia), Kirk and Spock are only one standard year apart. The notion that Spock must be older is not supported in any way by the televised series. The possibility isn't contradicted, either, but nothing we've seen on screen requires it.
About the only argument I could see is that, if they actually had known each other at the Academy, you'd think we'd have heard about it by now. But knowing each other in passing, or even having one or two assignments together, does not mean that they were friends there or shared many experiences that would become the subject of regular conversation, the way, say, Sisko's friendship with Curzon Dax comes up all the time in DS9.
McCoy, of course, is supposed to be a few years older than Kirk and Spock, but that doesn't preclude his being at the Academy at the same time, either. He was a doctor first, a Starfleet officer later; whereas Kirk and Spock can be assumed to have gone to the Academy in lieu of college.
Given that current canon suggests that Scotty is almost 10 years older than Kirk, it seems unlikely that he'd be a student at the academy concurrently; but it makes perfect sense, if they choose not to retcon this, that he would be an instructor there, or else an engineer on a ship to which Kirk and Spock are assigned as cadets.
In short...there's really no canon reason why this plot can't work. It's another question entirely whether it's a good idea, and I'm still not sure, myself, how I feel about that.