I would suggest having the Commvault admins configure it to skip your MDF / LDF / NDFs, and only back up "normal" files. Additionally, you can likely have them set things up so your BAK / TRN / DIFs get backed up more frequently than the other files.
Where I work, we do use Commvault, and it can "speak" to SQL for backups. The nice part is, it uses an Agent on the SQL server (OS level, not in SQL) to run a normal "BACKUP DATABASE..." command in SQL. The backup gets routed to a "virtual device" which funnels it across the network to the Commvault back-end.
Downside to this method is the usual, if your network has a flaky moment, you could have problems with the backup, although CV will "auto-resume" the backup. Not sure if it completely restarts though.
I have had to restore some backups from CV, it has checkboxes for all the usual options (overwrite, recovery / no recovery, point-in-time, etc) and works reasonably well. Not as fast as a restore from a local file, and (that I'm aware of) you can't restore from CV to a MDF / LDF without it being attached to SQL, nor can you get a BAK out of CV...