No they will transform even if the Moon is obstructed by cloud cover. Unknown dark forces related to the full Moon causes them to transform. However full illumination strengthens the Werewolf while complete cloud cover weakens them to an extent. That’s why Werewolf Hunters prefer cloudy nights.
It’s also a mistaken myth that they only transform on one night. The night of the 100% full Moon. In reality they transform during a Moon that’s at least 80% full. Although they are the peak of their power during the complete full Moon. So you have to be on alert all those nights rather than just one.
In addition there is one night a year when they require no Moon to transform into hairy horrors. That night being Halloween. Upon complete darkness on Halloween all humans afflicted with the Lycanthropy virus transform into Werewolves, and remain so until sunrise.