I don't think so. TOS did strive for a measure of realism and it doesn't make sense that an organization will hand one of its prized ships to a neophyte. Note that all other ship commanders seen in TOS were older and experienced men. Kirk would have to be tested and proven to be given such a prized command, not a lucky dumbass like nuKirk in ST09. Whats in "the book" is a reprint of the character's bio from the Writer's Guide which was handed to those who wrote for the show. Sometimes they deviated from it, but in this they didn't and the spoken reference from WNMHGB is consistent with it. Since it was never contradicted later on then it seems to be pretty established. And it makes more sense than any bullshit similar to what they did in ST09. And just because Kirk asked for Mitchell aboard "his first command" doesn't mean he got him. Maybe when he was given the Enterprise he had a little more pull to get an officer he wanted posted to his new ship.