When you open office 2013 and click "Open", you have 3 choices by default (Recent, OneDrive and Computer) and the possibility to "Add a Place".
I would like to create a add-in to add a custom place...
See, I develop a Electronic Document Manager software, and I provide a add-in to office suit, this would be another feature of the add-in.
Instead of "saving-locally-and-uploading-the-file-to-the-site" and/or "downloading-document-and-read", the user would just open and/or save to the site... I would use the Save/Open event to check if everything is right and the user has access and etc...
It kind of depends what you mean by 'office add-in'. Microsoft rather confusingly renamed the modern 'office store apps' to 'add-ins' at the Build 2015 event. However we also still have the old style VSTO 'add ins'.
If you mean a modern store add-in, then no, those only have limited access to read/edit the document via the office JS library.
If you mean the old style VSTO add-in, then I am not sure.