Good Question, the invoices that are archived are not necessarily the ones that are printed.
This is because the SD_VBRK archive object archives the raw invoice data, not the invoice image that is printed.
In my experience it is possible to create a customised Abap to re-print invoices in your specific format from the archive files. Have a look at the example read program S3VBRKAU for how to access the archive data files.
An alternative is to only archive invoices after they have been paid for a specific length of time.
There are documented user exits within the archive programs to allow you to write any extra validation you require.
Hope this helps