Drug induced sleep can be of two varieties, (1) "drug assisted" (mostly benzodiazepines, like lorazepam (Ativan), or imidazopyridines, like Zolpidem (Ambien), and (2) true "general anesthesia." Benzos assist sleep but because they are potent amnestics, one is less likely to remember a dream, even if you had one. Melatonin is not a benzo. It is an endogenous hormone, produced by the pineal gland. Melatonin is involved in regulating circadian rhythms, although it is not the main determinate. High doses of melatonin seem to be associated with more REM sleep and more dreaming.

"General Anesthesia" is not normal sleep and, rather, is unconsciousness produced by specific inhibition of neuronal communication (synapsis), whether by inactivation of protein channels on cell membranes, or by inhibition of GABA receptors, (a neurotransmitter). Deep levels of general anesthesia can flat-line your EEG, meaning your brain is totally shut down and is doing no synaptic work at all.
However, people may do normal sleeping after recovery from general anesthesia and they do occasionally relate dreaming during the period of recovery. In particular, the sedative/anesthetic Propofol is associated with some "erotic" dreaming and I have had some people relate rather vivid and interesting content. I had one older gentlemen who wanted to be put "back to sleep" so he could continue his "relations" with Gina Lollibrigida.

So there are two interesting things about the way this device works; a single electrode for the EEG recordings and a dry contact on that electrode. Its also shrunk down nicely, or course, but thats not super hard to do.

Unless people get really creative, the only way to get good recordings appears to be going invasive.