The whole Yorktown story was nothing more than Roddenberry's vanity speaking because that's what the ship was named in the original TOS draft.
Actually, it was Roddenberry's attempt to explain why there was another Constitution-class ship conveniently there and ready to go for Kirk. Having it previously been the old Yorktown
made sense for Roddenberry.
I'm inclined to disbelieve it for the simple reason that, as somebody already said, the actual Yorktown was in the same movie and likely had a full crew aboard (the captain was putting all "non-essential personnel" into stasis when the power went out).
Most of the Yorktown
's crew could have been stayed after the renaming or reassigned to a brand-new USS Yorktown
launched sometime after the Enterprise
-A. The same thing could have happened to the conveniently existing Sovereign-class ship that became the Enterprise