Unfortunately, relative URLs cannot be supported by the plugin as the document viewers (Google Docs Viewer and Microsoft Office Online) require absolute URLs to be able to render the documents.
Kindly note that by default, when you add images and other files also in a WordPress page or post, full URLs are used. It is recommended to search and replace the domain name everywhere in the database when you move to a new domain name. If you follow it, the PDF links also will be updated with the new domain. This way, you can make sure nothing breaks when you migrate to a new domain.
You have mentioned that the plugin works nicely for you. We are glad about that, and thanks for the comment. But the rating you have given because of the things that are not under our control – could badly affect us. Kindly consider updating it.