I looked at RCTs on clinicaltrials.gov and melatonin supplementation appears to result in slight, but to me significant, sleep improvements. Latency decreases by about 15-20 minutes and the percentage of time asleep increases by 5-10%. That's about 45 minutes a night. Doses used vary but are clustered around 1-4 mg.
I suffer from frequent insomnia and, on nights when I take melatonin I "seem" to sleep a little bit more (unfortunately I sometimes forget - I plan on correcting that). Very anecdotal and N of 1.
It is odd that government RCTs show a slight improvement in sleep yet the message I get from the media and doctors is that melatonin doesn't really do much of anything outside of jet lag.
This one is for a small number of diabetics and shows a small sleep improvement: clinicaltrials.gov/ct2/show...
A small number of insomniacs: clinicaltrials.gov/ct2/show...
Another study that shows slightly better sleep with melatonin: clinicaltrials.gov/ct2/show...
But it has a small study size and no baseline so hard to draw conclusions.
I also found one null study.
All in all, I wouldn't bet much on it, but melatonin "might" improve sleep quality. Sleep quality and quantity are important for general health and for the cancer fight.