A feeder that takes the stack from underneath gives you the document from the last page to the first. Drop it in: the thumbnails are already the right way round.
What it does not do: What the pages say about each other is not reversed: a “see next page” now points at the one before, and a table of contents keeps its numbers.
Nothing is uploaded. Cut your network connection once this page has loaded: the tool keeps working. How to check it yourself.