Yes, it really does. Thanks for playing, though.
Not really.. Not to the 99% of the rest of fandom.
I'm glad they didn't try to make the Constellation look like the AMT model. I do see your point about making the ship look "older" to justify the registration number, but there have been many other theories about this that could preclude the possibility of a difference in ship design.
With all the other effects shots in this particular episode, redesigning the Constellation seems like a pretty trivial pursuit.