No. Most gerbils are active in the daytime, and are therefore not nocturnal. The ones kept commonly as pets are active during the day, like humans, a lifestyle known as diurnal (the opposite of nocturnal). Some species are crepuscular, which means they are most active around dawn and dusk.
Note, however, that even diurnal gerbils such as the Mongolian still sleep frequently throughout the day, and during these sleeps they should be left alone. These small animals only live a few years, and they live at a much faster pace than we do, with swift movements and heartbeats many times quicker than ours. In effect, by sleeping and waking frequently they are packing several days' waking/sleeping into one 24-hour period.
Gerbils are active during the day, but still enjoy plenty of snooze time!
The fat-tailed gerbil, one of the species kept as a pet, is crepuscular in the wild, but has become more active during the daytime in captivity, in response to their environment.
Gerbils' day-loving habits are in contrast to the stubbornly nocturnal hamster - those fur-balls spend most of the day asleep, and tend to look for action just as the kids are going to bed! You could very well argue that the gerbil is a much better choice of pet for any child, on those grounds alone.