I doubt the JJprise-D, if such a ship even exists, was in the neighbourhood when the universes started to merge.
Considering the size of the new Enterprise (725 meters in length compared to the original's 289), let alone the size of...
The USS Vengeance, a top secret Federation Dreadnought - which is at least twice the length of the Enterprise. It's a motherf
ng monster! 1450 meters plus - by comparison the Enterprise-D is a puny 642 meters.
...I can't imagine the alt-Federation returning to the exact same design their Prime-verse counterparts do a century later.
That said, somehow the Mirror Universe NCC-1701 is identical to 1701-prime, despite the identical USS Defiant having emerged into that universe 100 years previously and fallen into the hands of the MU NX-01 crew.