Unfortunately, unlike ditto, the illusions of zorua and zoroark actually require some level of concentration to maintain. (This is why striking them once will dispel the illusion they’ve created.) As such, no, they can’t maintain the images they’ve created while sleeping.
On the other hand, if a zorua or zoroark has a particularly vivid dream, you might see them sleep-weaving. Just as a fascinating note there.
The Pokédex According to Bill 