I don't worry about a broody hen being able to get the chicks down. I've seen a hen get her chicks out of a 10' high hay loft. She said "jump" and they did, then hopped up and ran to her. Mine consistently hatch in nests as high as 4' off of the coop floor. Ny concern is can she get them up out of the tool box.
That is a risk. You need to make sure the chicks can follow the hen. Bedtime is mainly when I'd worry.
She should be very protective of her babies. Some broody hens might let you handle her babies if she is a pet and used to being handled, but there is a real chance she will flog you if you pick up one of her babies.
I'm not sure wild birds actually do that. I think that's more something that people say to get others to leave those baby birds alone. But no, broody hens will not abandon their babies if a human touches them. Absolutely no worries about that.