Short answer: With only PVEVMUser permissions, no.
There are a few permissions that come into play here.
PBS:
- The user on the PBS system, will need to be assigned "DatastoreBackup" permissions, which allow for backing up and restoring of owned backups. This user is a separate entity from the PVE user.
PVE:
- The user needs the PVEVMUser permissions on the VM to backup, restore, modify, etc.
- They also need PVEDatastoreUser on the PBS datastore and the storage which they will backup to, in order to read content and allocate space on both the datastore and the drive being restored to.