There is a way to save a document to Dropbox from within iAnnotate.
When you are in the document you wish to save, press the arrow (the curvy one on the upper left side). Select "Open In..." The app will have you decide which type of sharing option you want to perform: Annotated, Flattened or Original.
Once you select one of the three options, a pop-up box will appear. One of the options (at least on my iPad) is the option to "Open In..." Dropbox.
When you select it, Dropbox will open and you decide where in Dropbox you want to put the document. Once you decide, it gets uploaded and then it is accessible to anything that can access Dropbox.
Hope this helps.
Marilyn