Please consider this workflow as a new feature:
Select a chunk of text from a word processor (Word, Google Docs, txt or similar)
Right click, get a menu item “insert DOIs in PaperPile”
Selected chunk gets scanned for DOIs and DOI urls, which get added in batch to a certain folder.
This would make easier to import biblographies from manuscripts and papers.
@Ernesto_de_Bernardis something similar is coming in our renewed web-app – it will be possible to paste plain-text bibliographies (via Add Papers in the library) and detect/import citations from there to any label/folder of your choosing 
I don’t think we’ve considered doing this directly from documents yet, so I’ve added your feedback to the topic on our tracker.