Fixed (1.0.0.9)
Now there should be, first, a reasonable error message if you call the Add-in when there is no active document.
Second, you can now pass in the document to the Synchronize method (if not passed then active document is assumed by default)
I.e. now you can call it like this (where "doc" is the document you want to sync):
Application.ComAddins("BackSync").Object.Synchronize doc
The issue was that when you either open or close document, active document is Nothing.
I.e. now it should work also from DocumentOpened / BeforeDocumentClosed (if you pass in the document)