It can, but there are still references to Vader being Obi Wan's pupil in A New Hope, which makes it obvious straight away that vader is anakin (to people who've watched the saga in chronological order and know very well that Anakin was his only pupil)
EDIT: It would also mean cutting "when I left you, I was but the learner. Now I am the master". SACRELIGIOUS!
Now if only there was a way of giving Obi Wan a pupil that was a complete asshole.
Oh wait....