So when you squat you are carrying a large amount of weight on your back as we know and I'm trying to figure out if that holding that weight on your back and shoulders would build them, too?
If you are doing it in proper form, it'll build your middle back, lower back, glutes, legs and it'll also help strength the sides of the abs. Your shoulders and traps should see almost no change.
You do get your traps sore because of all the weight that is resting on top of them but you are not putting them under tension.
If you want to build your shoulders and traps, you'll need to choose a more specific exercise:
The lower back is the failure point of back squats, and gets a lot of work out of them. So yes, back squats build the back. Are back squats the best for the lower back? Not always; I find deadlifts slightly better for maximal loading, and weighted back extensions somewhat better for hypertrophy, but squats are a great middle ground.
I find that doing >1.25xBW high-bar back squats with a focus on scapular retraction and proper upright posture gives some soreness and progress to my upper back, probably my traps and rhomboids. This is tough to gauge since I almost always do squats alongside other exercises that work those muscles. Regardless, squats definitely aren't the best for the upper back, but they certainly do require and develop significant upper back strength. The upper back can definitely be a failure point for the back squat, as in fact we (probably) see in this recent question.
I don't find that squats do anything for my deltoids. I mean, I suppose I squeeze them a little? But the effect is practically insignificant. The deltoids are never, as far as I've heard, a failure point in the squat. Squats are not the exercise to do for bigger or stronger deltoids.
The squat affects the following muscles:
Although you may not think of the squat as a back exercise, the erector spinae muscle group contracts isometrically -- without shortening and lengthening -- during both the downward-movement and upward-movement phases of the exercise. The erector spinae group includes the iliocostalis, longissimus and spinalis muscles that span the length of your back on both sides of your spine, attaching to various structures therein. Although the muscles don't contract concentrically or eccentrically when you perform the squat, they are the primary spine extensors and also assist with lateral, or sideways, spine flexion and torso rotation ranges of motion.
The gluteus maximus muscle attaches to the posterior, or back, portions of the coccyx, iliac crest, ilium and sacrum on the inside of the pelvis on one end, and to the back of the thigh bone and the iliotibial band, or IT band, on the other. It is the largest of the gluteal muscle groups, which also includes the gluteus medius and gluteus minimus muscles. It facilitates hip extension along with the hamstrings on the back of your thigh. The gluteus maximus contracts eccentrically -- while lengthening -- to control the speed of the downward-movement phase of the squat, and concentrically -- while shortening -- to extend your thighs during the upward-movement phase.
The three muscles that make up the hamstrings muscle group -- the biceps femoris, semimembranosus and semitendinosus -- are also active when you perform squats. All three muscles attach to the ischial tuberosity on the back of your pelvis on top, and to the tibia bone of your lower leg, just below the knee joint, at the bottom. The biceps femoris also attaches to the head of the fibula bone of your lower leg. The hamstrings help the gluteus maximus muscle with hip extension, so they function in the same way when you perform squats -- eccentrically during the downward-movement phase and concentrically as you return to the starting position.
The rectus femoris, vastus intermedius, vastus lateralis and vastus medialis muscles are referred to collectively as the quadriceps muscle group. The rectus femoris attaches to the anterior inferior iliac spine, just above the hip socket, and the others attach to the thigh bone, just below the hip socket, on top; all four muscles combine at the bottom, attaching to the patella on the front of your knee joint. The quadriceps muscles serve as the primary knee extensors, increasing the angle between your lower and upper legs. Like the hip-extensor muscles, they contract eccentrically during the downward-movement phase of the squat and concentrically during the upward-movement phase.
Squat is doing almost nothing for shoulders as the shoulder muscles and trapps are acting as stabilizers for the bar.