This answer addresses your question about a link between norepinephrine and melatonin, but I have nothing to say about depression.
In vertebrates, the link between norepinephrine (NE) and melatonin lies in the regulation of the melatonin biosynthetic pathway.
Arylalkamine N-acetyltransferase (AANAT) is an enzyme in the biosynthetic pathway for melatonin, and controls the diurnal rhythm of melatonin production in the pineal gland. NE is released as a neurotransmitter by neurons innervating the pineal gland, and which themselves are regulated by the circadian pacemaker of the hypothalamus. One of the effects of NE on the pineal gland is to elevate the transcription of the AANAT gene via adrenoreceptors and cAMP levels.
The paper cited below describes this, and other relevant diurnal rhythms in the viscacha, a rodent of the chinchilla family. This animal was chosen because it has an interesting diurnal behaviour pattern with two apparent peaks in melatonin biosynthesis. It's a good starting point for further research into the literature on this topic.
Calderon,C et al. (2008) Daily rhythms of norepinephrine, β1-adrenoceptor mRNA, serotonin, arylalkylamine N-acetyltransferase mRNA, arylalkylamine N-acetyltransferase and hydroxyindol-O-methyltransferase activities, and melatonin in the pineal gland of viscacha. Biological Rhythm Research 39: 93-107