From Asana Support
"That’s a great question and you’re right, it is not possible to work collaboratively on a document, although I can certainly understand how this could improve Asana! For now, you can only attach hard copies of files from different sources. The file would then need to be downloaded and worked on separately.
To be completely honest, we don’t have any immediate changes for this planned in the near term."
It seems to me that live linking to live docs in Sharepoint or Drop Box, or for Mac people, iCloud, would be an incredible benefit. If you agree please reply and add your clamorous agreement!
Also the Technology behind Drop Box is not rocket science, I would think Asana could “roll their own” collaborative editing feature, or license the the service offered form another party and incorporate it in Asana it .