Yea, STID is set 1 year after ST'09.
I think most great bonds are formed well before 1 year in the trenches together. Matter of fact, most great bonds are formed pretty early in a relationship.
I can't imagine a Captain and First Officer who haven't formed a great bond within a year serving together will ever form a great bond.
I think NKirk and NSpock's relationship is "barbed" as opposed to being shallow. NKirk and NSpock have bonded in the fact that NKirk avenged the destruction of Vulcan, which NSpock is grateful for. The two of them have a prickly relationship, however, because NSpock is trying to do things by the book and NKirk is fully willing to engage in criminal activity as long as it's for the greater good. Falsifying documents goes above and beyond what should be expected from bending the book and OKirk would have beaten the crap out of his younger self for that (or phasered him on stun).
They're friends but Kirk is the guy who wants to cheat on a test (and, in fact, is literally that guy).