Rarely do fan fits become better than the original story. It's subject to changes or wish fulfilment.
Is it possible? So far ghost in the shell: Stand alone Complex surpasses the original Manga and I dare say even the film adaptation. But the difference there is a huge team.
I believe if someone who is skilled, passionate, but also has a neutral team that knows how writing works, then I'm sure it's possible.
But I doubt anyone would ever dedicate that much time on make fan fiction. Fanfiction is the deviant art of writing.
GIT:SAC was fanfic? I though that was done by pros?