It's a personal choice. Some separate broodies, and others want flocks that can coexist so leave them alone. Same for where they raise their chicks. I have let 3 batches set eggs and raise their babies in with the rest of the flock from day one successfully, but this does take a good mama hen who will protect her chicks, and not all of them will. People have let broodies hatch chicks in hay lofts and had them survive, but most would move them lower to the ground. Moving can upset them and make them stop setting, though. I have moved some but did so by keeping them in the same nesting box and moving the box. I tried moving them to another next box but they would not accept it.
If you do not separate, it is wise to mark the eggs (Sharpie works well) and check to be sure someone else isn't adding eggs to the batch. I usually have to remove added eggs during the setting period.