The zotero-reference plugin is the nearest to doing that. It will read an article's reference list by parsing the PDF, or loading it from Crossref. It puts the list in a new References tab in the PDF Reader. It highlights those references already in your library if it can match DOIs. For any other reference you want to add to your library, it will take you to its article web page by DOI (for downloading via the Zotero Web Connector in the usual way).
https://github.com/MuiseDestiny/zotero-reference