I believe Office and Dropbox integration is only for Office Online and not for the desktop versions of Office. I looked up the File -> Open menu in the Winword.exe 2016 and didn't see a way to add any other place other than One Drive and Office 365 SharePoint.
This leads me to believe that the One Drive and Sharepoint integration with the desktop versions are perhaps OAuth 2.0 implementations. And the Office Online and Dropbox integration is a WOPI one, Dropbox being the WOPI host?
Could you please confirm?