I personally find that doing stabiliser while film is still in the reel is a good idea, though I take the reels from the tank and do them individually as Diapositivo suggests. If you unspool the film (in 120 at least) and slosh it around gently in a container, the corners of the roll will scratch the soft emulsion - that one I learned the hard way.
Not just, but if the film is a 135 the coils will tend to come very near to each other (difficult to explain in words: just try) thus not favouring a proper bath of the film. In order to be sure that the film is well soaked in the bath one should take some tweezers and separate the coils. I prefer keeping the film in the reel because that way I am certain that the film is well soaked. YMMV.