I think it is fine to check on the baby, but I would only take it for short time periods and make sure momma takes it back without any problem. She probably is the best one to raise it if you can let her.
Chicks raised by broodies tend to be more afraid of people. I'd personally try to handle the chick a bit everyday, offering treats to Mom and chick too. She can do most of the work, seeing as the is living brooder, but unless you handle the chick, don't expect it to be a friendly adult!
How friendly is your broody? Mine are very friendly, they come running up to me as soon as they see me and start clucking for the babies to come over too because I usually bring them treats. The babies are about 5-6 weeks old now, and now usually beat momma to me when they see me. They are a lot more friendly than my brooder raised chicks who didn't start to like me until about laying age.