I have hatched two broods of chicks under hens. I must agree that this is easier by far than raising them inside by myself. The chicks weren't as friendly as my hand raised chicks, but they came around later, once they figured out that I was the bringer of treats!
Both times, the hens had the chicks out among the other chickens within a few days. Everything was fine for us. The other hens were curious about the chicks, but they never tried to hurt them. The rooster was a jerk, stomping his feet at the babies, but again, he didn't actually try to hurt them.
I have heard horror stories about the other chickens killing new babies, though, so I watched mine closely at first, to make sure that didn't happen. My chickens are pretty laid back, and they have lots of room to roam, so I don't worry about that anymore.
In short, it depends on a lot of things. You'll never know how good of a momma your hen will be until you let her try. You won't know how nice your chickens will be to the babies, so keep a close eye on them at first. And be prepared in case things don't work out well. If the other chickens are misbehaving, you'll need to separate momma and babies, and if momma isn't doing such a great job, you'll need to bring the babies inside and raise them yourself. If you have already thought about what you would do in those situations, it will cut down on your stress should things go awry.
Good luck with your hatch, and good luck with your new chicks, no matter which route you choose!