There is a lot of confusion as to which ship the Enterprise A was before, I have heard that she was the Yorktown, but have also heard she was the Ti-Ho. I think the Ti-Ho was a complete new build though, before being re-named Enterprise.
I have heard that too: Yorktown is the ship that Roddenberry was telling people was renamed Enterprise A, but that doesn't make sense given that in ST IV, they say the Yorktown was adrift and they were getting ready to deploy the solar sail, when the Whale Probe rolled through Federation space near the beginning of the movie. It really seems unfair to unseat that captain and crew to give the Yorktown to Kirk, and then to add insult to injury, rename it!
And with Ti-Ho, from I think MR Scotts guide to the Enterprise or something similar, a brand new ship, being renamed Enterprise-A, it still doesn't make sense, when it was decommissioned 5 or so years later.
So to me, the thing that makes the most sense to me is the Enterprise-A was a newly refitted Constitution Class ship, that was around the same age as the original 1701, and then renamed Enterprise-A .