Just seems a bit daft to rename an already-serving starship from Yorktown to Enterprise-A just for Kirk and his crew. It's more likely that this ship was about to be commissioned Taiho (yeah, I know the book said Ti-Ho...) and was changed to E-A at the proverbial last minute.
Actually, that's no more likely than if the ship was the Yorktown
. Starfleet wanted to reward Kirk with a new Enterprise
and chose another Constitution-class ship. It could have easily been any vessel of that design that was in dock at the time, including the Yorktown
In regards to the origin of the Enterprise
-A, there's more than one theory that works.