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It depends on space and the personality of the individual chickens involved. The more space you have the less likely you are to have problems. That seems to be true about everything chickens.
A good broody will protect her chicks from the other members of the flock. If another chicken threatens her babies, a good mama will reprimand the offender. She normally only has to do this once or twice and the others learn to leave the babies alone. If you interfere while she is teaching the lesson, you make it harder on mama and she will have a harder time teaching the lesson. You'll note I said a good mama. Not all broodies make good mama's so it is possible to have problems. They are living animals.
Most of the time, the offender is another hen. A good rooster will defend all members of his flock. There have been cases where a rooster looks after chicks if something happens to the mama or she abandons them too early, going so far as to keep them warm. That's a bit extreme and not really normal, but it does happen. And not all roosters are good flock masters.
I personally think chicks raised with the flock develop better immunities and have less severe integration issues later. Mama takes care of the severe integration issues for them. They will still have to sort out the pecking order on their own as they mature, but I feel the dangers of that are much less than the dangers of integrating young chickens with the existing flock.
I will mention that others quite successfully do it other ways. It is a personal decision, based on your philosophy and set-up.