I know cats are nocturnal, but cats seem to sleep during the day and at night, so I'm really not sure ...
It does matter if you have the light on or off for cats, or any animal that sleeps. Inside cats' brains along with mammals and some reptiles' brains, they have what is called the pineal gland. This gland has been shown to be very sensitive in its reaction to light and production of melatonin which supports animals in hibernation as well as normal sleep. The pineal gland's reaction to a light source is that it stops melatonin production. This is the reason why we get sleepier at night as well as during the winter time because the absence of light increases the production of melatonin.
This sensitivity to light is not limited to just humans but also cats. It depends on the location of the pineal gland in different animals, as well as the degree of reaction in production of melatonin, but still there is a degree.
Lights off is good but also try to make the period of time for sleeping habitual. That means try to keep it where the cat knows it's supposed to go to bed. If you have no set time, the cat might find it harder to sleep, especially with extra energy it might have.