The answer is (said in a Dr Bones McCoy Star Trek voice) "Yes Jim, but not as we know it".
I have kept fish since the tender age of about 5. I am facinated by all things "underwater" and often study my coral tank at night to see all the weird and wonderful beasties that come out to play.
Anyway, I do this with the aid of a red LED so as not to scare stuff. The fish are often tucked away out the main flow, between rocks etc and just hanging there. They lose there colour and become very pale.
If you watch them it is almost as if they are asleep, but with the eyes open. If you then shine the LED at them after a minute or two they sort of "wake up", regain there colour and start to swim about.
I guess they are just shutting down there systems but staying alert enough to recognise danger.
On another note, I was up at McDuff aquarium at the weekend and they have a few Sea Trout in with Mullet and Bass. The trout were all wedged under weed on the bottom, not moving. Exactly like my fish do at night.