If you have a backup of your iPhone made before the note disappeared, then yes the note can be retrieved. One thing to note, however, anything added to your iPhone after the backup,was made will be erased when restoring from the backup.
If you don't have a backup or you don't have the note stored elsewhere other than your iPhone. It can't be restored.
What is the default account for notes? Go into Settings>notes to see. If it is Yahoo for instance, things have turned up under a misc folder in Yahoo mail.