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I've seen a few apps which read IMAP mailboxes, such as mailPro and OneMail Plus and (probably closer to the OmniFocus use case) ReaddleDocs.

But another idea occurred to me a few days ago: what if Mail added document interchange support for the mail message you were currently looking at rather than just its attachments? That would require no new iOS APIs and no OmniFocus special cases, but would make it easy for an app like OmniFocus to advertise to the system that they open email messages which would give us an easy way to solve this problem.