Is it possible to re-compose the same orchestral music from the sound track?

I am sure it is.  Mozart was said to have done so after just hearing a
live concert once.  With a recording, the task should be much easier. 
People studying in Germany to be conductors are asked/required to
attempt to do so for a much shorter excerpt to demonstrate or to
school their "ear" as practice to recognize if the performers are
playing/singing the right notes.  That is a little different, but they
are given the excercise.
With the experience to identify individual instruments, and the
possibility of listening the the music again and again  - plus
increasing bass or treble to accentuate the instrument being followed,
the task for a musician would not be too difficult  - certainly not
impossible.

Would it be possible if there is vocal singing with the orchestral performence?