I doubt it, I'm afraid. The attachments are actually encoded in the email body, and when you open them a temporary file is created for you to view. Since it's only a temporary file, there's not much point in making it writable.

The only way it would make sense for it to be writable is if, when you save the changed document, this new attachment somehow written back into the body of the email. But it's hard to see how Outlook would have any control over that, plus it would break what I believe is a deliberate policy that you can't change received emails (i.e. what you see in your inbox is always an accurate reflection of what was sent to you.)