Not the Academy, but it didn't happen until he was on Earth in 2261 for whatever reason he was on Earth that year.
Correct. It was explicitly stated in "This Side of Paradise" that Spock's relationship with Leila Kalomi , such as it was, was six years prior to the events of that episode, thus 2261 . . . or, if SNW follows a one year per season rule, we shouldn't explore that until SNW Season Three.