I've had 5 or 6 broodies raise chicks in with the rest of the flock. In some cases they were separated for a day or two but mostly they hatched right in the coop.
That's not to say it's 100% safe, of course. Mamas are normally very protective, but you can never predict how an individual will act.
Bringing them in the house will create the primary situation I wanted to avoid, namely trying to reintroduce what to them will then be strangers. This will likely be a problem for the mama as a lone hen but even worse for the chicks. The mama will usually mother and protect the chicks for only 4 or 5 weeks. They will need another 3 months or so to get full size. Mine have always known how to avoid anything serious on their own, by staying together, though they are low in the pecking order, and they have a large coop and maybe 70' x 70' yard to escape in. If raised separately, I believe most people keep the chicks in a separate "grow out pen" til full size when the mama wants to stop mothering and go back to the flock.