Yes.  Backup Exec has a TSM interface that will do just what you describe.
I tested it a couple of years ago, worked fine.  (We ended up not using it
because there was just too much data to send across our network at the time,
but that was a network issue, not a problem with the Backup Exec interface.)


At the time I looked at it, the TSM(ADSM) interface was an extra cost
option, but that may have changed since.  It's pretty easy to set up, they
provide explicit instructions.