Maybe I misinterpreted the question. Is it the same ship from TOS? Not remotely. Is it a ship that could be 'refit' into the ship we saw in TMP? Not any more easily than the classic ship was. Assuming the saucer is a direct number-by-number copy of the one on the TMP ship, which is just what it looks like, the rest of the thing is too small, with the exception of the engines, which are Dolly-Parton's-hooters HUGE by comparison.
"Now I did a job -- and got nothin' but trouble since I did it, not to mention more than a few unkind words as regard to my character, so let me make this abundantly clear: I do the job... and then I get paid. Go run your little world."