Yes, loud children will make a bird to scream louder. All parrots are highly social species which live in large flocks made up of their immediate and extended family and they all have loud 'voices' because they need to be heard over all the other birds so when you put, say, loud music on, they will scream louder so as to be heard over it - and it's the same thing with children, if they scream, the bird will scream, too.
Now, I don't know how old your baby bird is but, if it's younger than 6 months, you should be feeding it soft food. I also don't know what you mean by 'enclosed', are you referring to a cage? Because if we are talking about a tiny baby and the 'enclosure' is something like a small animal habitat, it should be OK for now as nests are small but if that is the size of the cage, you are going to need to buy a MUCH larger one. Rule of thumb is 5 times the bird's height (from head to tip of tail) for the height of the cage, 3 times their wingspan (the distance between one tip of a completely open wing to the other tip of the other wing) for the width and another 3 times their wingspan for the depth.
As to the bird becoming independent... well, I am afraid that this is not going to happen with a GCC. They are extremely needy little birds which need much more out-of-cage as well as one-on-one time than any other species except for the cockatoos.
But as far as the screams go, that should be a non-issue as long as he is getting the right food, a solar light schedule and enough attention because they only scream when they are unhappy. I now have one GCC, a female named Codee, but I had four of them altogether (the other three were rehomed -the two healthy male and female which had bonded with each other here to one home and the other, a handicapped male, to a wonderful couple with no children who adore him- and I still keep in touch with their owners) and none of them screamed after a few weeks with me. You also hardly hear a peep out of Codee all day long although, come dusk, you can hear her screaming for all she is worth asking for her dinner