In my experience, it doesn't have to be done at night. A broody hen is happy to have eggs anytime! We have banties, and they have sometimes built up a clutch of 18 eggs or more to sit on, out in our yard under a bush. We have never let them keep that many under them in our henhouse nest boxes, but maybe it would be okay with a standard-size hen.
My concern would be if the nest box is big enough to hold them all comfortably, without eggs banging into each other too much. We have occasionally had eggs get cracked too early.