Has anyone heard of someone getting their work published by a journal, or some other form of publication, because their unpublished draft was discovered on Academia.edu?
There's a role in publishing called acquisition editor, sometimes also called commissioning editor (the roles of these two are, strictly speaking, different, but they're almost synonymous). The job of these people is to find things to publish. This could, for example, be an otherwise unpublished paper suited to the publisher's [journal], or perhaps commissioning an author to write a review on [topic].
How does one go about doing these things? Different acquisition editors will do things differently. Searching academia.edu is definitely a reasonable way. If one finds an unpublished article on academia.edu that's 1) a good paper and 2) suited to one's journal, one could certainly write to the authors asking them if they want to submit. So although I don't know any paper that went through the process you describe, it's possible.
Caveat: these papers still have to be peer reviewed. I'd be skeptical any paper went directly from being discovered to being published.