I haven't personally tested, but there is a tiny chance it might work. From what I can see the File Away plugin generates shortcodes, which parse/display the content on the front-end. The problem is that the data is not actually stored on the page, only the shortcode is.
However the index table engine was built for cases like this. It's basically allows to index words out of the actual post content that is displayed on the front-end, including executed shortcodes content.Best,
If you like my products, don't forget to rate them on codecanyon :)