ETA: looks like the ref to NCO Colt as an Ensign was a one-off, tho the spelling of Ilyria as "Illyria" and as a colony I suspect was due to an old error at Memory Beta.
Not necessarily. There are a number of clear differences from canon here. Garison is a lieutenant instead of a chief petty officer, Pitcairn is chief engineer instead of transporter chief, the Klingons already have a prototype cloak in the 2250s, and there's even a reference to the Ferengi. Plus it's evidently before "The Cage" yet Colt is already Pike's yeoman, rather than the replacement for the one he lost on Rigel VII immediately before "The Cage." I was confused at first, until I read the author's note at the end, where Stern says that the new film continuity "freed [him] of the need to write specifically to one vision of humanity's future" and that the book shows "the Enterprise
as it might have been under Captain Christopher Pike." He calls it a "prequel" to the movie, though it can't be, since the movie showed the Enterprise
's maiden voyage. So it's not quite in the Prime universe and it's not quite in the Abramsverse. It's apparently sort of a stealth Myriad Universes
tale, an alternate take on Pike's captaincy and on the astropolitical situation of the 2250s.
It's an interesting approach. I'd imagine it's a product of the period when the editors weren't sure how to deal with the new continuity and were developing projects adaptable to either timeline, or at least not specifically bound to either one.