Different agents will handle this differently. For File system backup, CV tracks files backed up in the index, so depending on how far the backup is and the state of the index will determine if the backup (when resumed) would start from the beginning or pick up where it left off when the reboot occurred.
As far as the Oracle iDA, there is less granularity, but depending on the configuration of the backup and RMAN options selected RMAN can resume a backup based on the backup piece level. So if the database is backed up using 10 backup piece handles, and get interrupted on the 6th piece, it can be restarted with that 6th piece and skip pieces 1 through 5 (that have already been backed up).
Other database agents may have to start over from the beginning... it all depends upon the API being used for the backup.
Ernst F. Graeler
Applications and File Systems