I think it's safe to say that each graduating class has, at least, several thousand cadets. It is entirely possible that they never met, or was at most fleeting, ala Shatner's version. My high school graduating class had around five hundred in it, and I only knew maybe twenty.
Agreed. And Spock was also a big nerd who probably kept to himself while Kirk was devoting his time to chasin' skirts.
This might also explain why Spock never met John Gill- he didn't take his class. There are loads of lecturers at my Uni who I never met.