I was wondering since this Enterprise in the Abrams TL was a built few years later it probably should have a different registry number. But it doesn't. What would be a possible in universe explanation for this?
The registry number can be assigned years in advance, and not dependent on the actual build date. I'd suppose the plan was to build 1701 sooner, but after Nero's incursion, she went back to the drawing board for major upgrades, which delayed completion.
That was my thoughts on it too. The ship was launched in 2245 in the Prime Universe. It was probably on the same schedule in the AU, but after Nero's incursion, the ship was redesigned and jacked up. This resulted in the ship being built and launched later. Now I have a mental image of a Starfleet engineer holding a blueprint of the classic Constitution design, checking his email, and balling up the blueprint sheets to throw them out while swearing.
^ Absolutely, that was my favored explanation as well. We might even take canonical evidence from the fact that (as far as we can tell) she's launched brand new under Christopher Pike's command in the AU, when it's generally accepted that she had existed prior to this by some years in the prime universe and was once commanded by Robert April before Pike took over.
Also worth noting is the appearance of a prior Enterprise in the comic run, also 1701. Even if it's not canonical, it does give us an indication that the opposite happened. That, what we know as the original Constitution class was given some quick rethinking in the wake of the Kelvin attack and was built and launched ahead of time by eight or nine years.
I wouldn't look too far into the fact that the comics showed April's Enterprise with 1701 for its registry, or even the design of the ship. Knowing IDW, it was likely a mistake. After all, they have shown the Abrams Enterprise with TMP style nacelles and the registry NCC-1701-D to say nothing of how often we see 24th century LCARS computer displays. They've shown characters slapping the Starfleet insignia on their chests to communicate and have been so inconsistent with the appearance of one of their characters created for the comics to the point that in the recent comics she has different colour hair and skin. IDW comics are not a reliable precedent for anything
Regarding Countdown to Darkness, I don't think there is any image of April's ship anywhere in that comic, not really. The ship shown twice when April gives his backstory is simply Kirk's own ship! I mean, the writer and the artist may have intended for it to be April's, but they fail completely. The design is identical to Kirk's ship, within the limits of the comic's overall artistic detail at least. And nothing in the dialogue or imagery actually indicates that it would be April's rather than Kirk's. Timo Saloniemi