Much would probably depend on what Kirk is supposed to do with this ship.
Pike was supposed to use the brand-new NCC-1701 as the Fleet's "newest flagship". What does a flagship do? Is Kirk scheduled for promotion tours, or task force coordination missions, or just run-of-the-mill exploration and defense but with panache? Is his mission different from Pike's even though the ship is the same?
In TOS, much of the allure came from us watching a group of professionals who knew their job, their hardware and their colleagues well enough, even though their working environment and job challenges were beyond bizarre. In nuTrek, Kirk isn't a seasoned veteran, but rides on intuition and general superheroity. It probably doesn't matter much what sort of a ship he is given, then.
If Starfleet feels NCC-1701 needs repairs, it could decommission her for those, send Kirk out in a shuttlecraft, and expect universe-saving heroics anyway. OTOH, Starfleet would probably also feel Kirk can triumph in a ship that hasn't been properly repaired - or in a ship that has undergone untested modifications.
I doubt the actual specs or status of the new NCC-1701 will feature in any way in Kirk's quest to defeat the Cumberbatch character...