if database is added within same lun's as other database, you should be good to go an create a scheduled task without the database names in the syntax.
the new-backup cmdlet accepts the -Database parameter as an optional parameter
as per page 148 of SMSQL 7.2 AG:
"If you do not specify the database parameter explicitly, the cmdlet backs up all the databases from all the SQL Server instances in the host. If storage other than NetApp storage exists on your system, the cmdlet omits databases located on that storage. Databases incompletely configured or databases in incompatible states are omitted when not explicitly provided with this parameter"