Looking around I see animals - ants, bees, birds, lizards, roaches all the way up to humans appear during a part of the day and not other parts. I would guess there is a sleep/recovery cycle involved.
Is there any multi-cellular organism with a nervous system, on record, that works without sleep/rest?
Well, you may want to re-state your question. There are numerous multi-cellular organisms without a nervous system. So you could say that they never sleep: sponges, plants, mushrooms.
This paper on the evolution of sleep concludes:
A phylogenetic evaluation of sleep demonstrates that all mammals, birds, and reptiles engage in sleep, and evidence for sleep in amphibians, fishes, and invertebrates is strong if not certain.
So it seems that once you have a nervous system, you also have some rest periods. However, it may not be clear if the rest periods are dictated by the lifestyle (e.g. nocturnal foraging) or by a requirement to "recharge" the nervous system.
