Boy do we have different opinions on this. I personally find the less I interfere with Mama and her kids the less damage I do.
They don’t need to eat or drink for three days or more so if Mama is not immediately feeding or watering them it is not cause to panic. That’s the way nature designed them so Mama can stay on the nest and hatch the late eggs. That’s why they can be shipped in the mail so successfully.
When I do have to pick up a chick, practically any broody goes into attack mode, wings spread, feathers fluffed, and all that. Seldom do they actually attack. I kind of like a hen being protective of her chicks but I don’t try to handle my chickens a lot either, just when I have a need.
Can you pick up a chick? If you want to, go ahead. If the broody attacks, just don’t panic and do something that will hurt the chick. Stay calm and things will work out.