Not sure, but you could certainly use this mod ((link)) for adding your inventory code/serial/ID.
Then you could possibly modify include/client/viewticket.inc.php and include/staff/viewticket.inc.php to present the inventory code/serial/ID as a link back to an asset management software such as Kwok ((link)).
Likewise, you could use one of the new features in Kwok to create a link back to a "search" in osTicket that would list out all tickets (open or closed or both, depending on how you configure it) that contain that Inventory code/serial/ID.
What ya think?