We do essentially the same as Lord Flynn. Broodies with eggs go into separate secure rearing units. The broody is separated when the chicks are 6 weeks and put alongside their intended coop and run occupants to become familiar with them and build up their strength. We've tried putting them straight back but they get badly bullied because their original flock has forgotten them- always difficult introducing one hen. The chicks get to laying age, so 26 weeks, before they get added to an existing flock.
We've had a chick damaged by the broody, so it can happen even without a cockerel there Sheepandponies.