The reason for the behaviour is that the copy will only copy entries from tblProperty (that contains published property data). An unpublished page will not have any data in tblProperty (the unpublished property data is stored in tblWorkProperty) and hence no data is copied. The reason for this behaviour is that when a copy is performed we do not want to copy all versions of the page just the published version.
However I think this is a bug and have reported a bug for it.
Posting an update since we got a question to the support about this. The behaviour is "by design" for CMS6 and 6R2 but the functionality has been rewritten for CMS7 to support copy/paste for unpublished pages as described above.
When my client copies and pastes an unpublished page, the new page is blank -- it has a title, but no other data from the page it was copied from. I've confirmed this behavior on a couple local installs.
Is this behavior by design?