They definitely have some kind of sleep state.
I've witnessed what Digger and Paradoxica mentioned with all my Religiosas, no exceptions. They do this kind of rest generally at dusk/early night hours and then become more active later in at the middle of the night.
I think this behavior is perfectly acceptable in the wild. Knowing that one of the worst predators of mantids are bats, standing completely motionless is the best defense.
Also I've found that they barely or don't react at all to visual input while in this state but they do wake up with surface vibrations, even tiny ones.
So with aerial assault out of the equation, they still have their vibration sensors on alert for terrestrial creatures.