No
Backup Exec does not attempt to find a tape with enought space.
The tape it selects is based on a management philosophy called ADAMM (Advanced Device and Media Management.)
If your job is set to Append, Else Overwrite, then BackupExec will look for the tape in the target media set that has the oldest creation date, and is still within the Append Period
if your job is Overwrite, then mo matter how much data is on the tape, the job starts writing at the beginning
See
http://seer.entsupport.symantec.com/docs/192265.htm Advanced Device and Media Management (ADAMM) Information which includes An explanation of the "Overwrite Protection Period" and the "Append Period