Question : Problem: Can Backup Exec backup data that resides on a SAN to a tape drive on a SAN without tranversing the LAN?

In addition, does the server to be backed up that resides on the SAN need to have any special agents or options installed on it? Does it become a media server?

Answer : Problem: Can Backup Exec backup data that resides on a SAN to a tape drive on a SAN without tranversing the LAN?

I believe that the Backup Exec SAN shared storage option is what you're needing, assuming that the server you have Backup Exec on is attached to the SAN.
It's the next to last one on this page:

http://www.symantec.com/business/products/agents_options.jsp?pcid=pcat_storage&pvid=57_1

http://seer.entsupport.symantec.com/docs/300231.htm