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It really depends. I find broody raised chicks that are out with the flock from day 1 are less friendly. 
I sometimes let broodies stay in the flock but have more recently begun separating them into brooders for the first month or so. So they are in a brooder on eggs, hatch the chicks and stay with them at least a few weeks, hopefully up to a month depending on what else is going on. Get your wanna be broody hens nice and friendly FIRST. If your broody momma comes running to you for food, so will her babies! They learn fast. 
I do very often take the broody momma out after a few weeks. Then the babies have a couple more weeks in the brooder under a heat lamp where they can get a little more used to me. 
But then again, I don't handle my birds much so friendliness isn't a huge thing. ALL of my birds, broody raised or not, will come running for treats when I call them. Do I pick them up and carry them around? Not usually. I consider my birds friendly, but they have zero interest in being grabbed and picked up.
Good info, thanks!
I completely agree! My birds all come for treats so I can count heads and make sure everyone is moving properly. 
  
And if something needs more investigation I do it when they have gone to bed. Personally I feel that if I wanted a lap dog, I would have bought one! 
I take the opportunity to go and talk to my broody every day and stroke her fluffed up feathers. This way even the most flighty will become used to me and the babies will be fine with me. 
And mama doesn't mind too much so long as I don't try to take the little ones away!