Background uploading is already possible with an extension, make sure the server has the Zimlet and your browser has the xpi installed:
Zimbra Gallery - Drag and Drop Firefox XPI
While uploading you can continue to work on the message.
By saving to drafts before navigating away it'll still upload.
Do something else, and then visit your drafts when the browser stops 'spinning' and it'll be ready.
(ZCS 6.0 will create tabs for each message on compose so this navigating away won't feel so 'wrong'.)
There are several RFE's open on the DnD extension that you may wish to vote for:
35570 bundle xpi on server
27153 multi-browser/platform
24794 detached compose windows
24694 progress indicator
38575 drop zone entire compose area
For regular 'attach files':
7862 background upload
22503 progress status
18678 cancel upload (currently just closes dialog - it still processes upload then removes)