I have not tested this end-to-end, but looking over the features/options it should be possible to post a PDF to FaceBook from Pages indirectly through the DropBox app.
This results in a link, not an actual file upload. That means if you later delete the file from DropBox it will break the link in FaceBook. I'm not sure if a PDF file upload (local storage on your FaceBook page) is possible. The usual tools upload pictures and videos. I'd have to look into it further.
In Pages select the Open in Another app option, select PDF as the format, and DropBox as the app. When the file finishes uploading, open the DropBox app, select the PDF, then use the share icon (box with an up arrow) and select FaceBook to post. You can choose add a comment, enable a location, and limit the audience before sending.