We have to wonder about warp specialist Kosinski in "Where No One", I guess. He gets to wear a Starfleet uniform, complete with an exotic-looking square collar decoration, but for some reason doesn't warrant a communicator pin. Most visitors don't get Starfleet clothes, although some might get a Starfleet communicator for convenience.
Has there ever been a reference that you know of, to the population at the Academy at any given time?
Nothing explicit on screen. What we know of class size might help, though.
That is, if every hero was credited as the best of his or her class, and knew each other through coincidence, we'd have to believe in a fairly small school. But thankfully, that's not how Trek works: say, in TNG, Riker was the eighth in his class, no heroes were classmates, and they know each other not through coincidence but because the Federation Flagship draws in the best and the brightest and the oddest. Similarly, in TOS, Kirk knows some fellow skippers, but only through them being fellow skippers; his only meeting with a former schoolmate is in a fantasy.
Data claims he graduated from a "class of 78", and since that in retrospect can't be a year reference, it seems he had 77 classmates who could testify his rank isn't purely honorary. That doesn't mean only78 people graduated that year, though - might be every year consists of a hundred parallel or intertwined classes, and the annual output is in fact 8,000 officers rather than 80.
Also, some teachers and lectures are "common knowledge", but nothing is universal, and there's always a hero who doesn't know what the other one is talking about when old studies, students and teachers are mentioned.
So basically the writers have steered clear of writing themselves in any sort of a corner here. Everybody knows Boothby, but that's it; otherwise, the Academy might hold a thousand students at a time, or a million.
Timo Saloniemi