Probably not. If everything was not included in the backed up disk image you are probably sunk as usually the restore procedure will format (wipe) the drive before restoring.
I use Acronis True Image to make backups, but I do complete hard drive backups. Then if I have to recover from a backup I have everything that was on the hard drive. There are some backups that only backup certain files or there are "incremental" backups that only backup what has changed since the last backup. The incrementals can get confusing so I only use the full complete hard drive (all partitions) backup method.