Update for Revit 2014 API
This is now possible with the Revit 2014 API. If you download the Revit 2014 SDK there is a sample project DuplicateViews which has a class called DuplicateViewUtils
that contains 2 functions, DuplicateSchedules
and DuplicateDraftingViews
which allows you to copy those 2 types of views from one document to another. The key component is the ElementTransformUtils.CopyElements
function which allows you to select a from and a to document for your copy.
Response for Revit 2013 API
I got a response from one of the Revit API gurus, Arnošt Löbel, and he said that this is not currently possible with the Revit 2013 API but that it has high priority for future releases. Only time will tell if this feature gets included...