Weightlifting shoes can aide in explosive movements such as when performing the olympic style movements and the flat surface they provide are great, becasue they create a more solid foundation, this is especailly important when you are under a lot of weight. As for using them during a back squat, they could be deterimental to you technique. You want to make sure that you are planting your heels into the ground when you are on your way down, you also need to press through your heels on the way out of the hole. As for bringing your center of gravity forward, they can definately do that. The height of the heel serves as an extention to the tibia(lower leg bone). Which can put your weight more forward, unless you have a longer femur(upper leg bone) to compensate, if you have extremely long femurs it will allow you to bring your hips back far enough to stay centered over mid-foot.
So in essence, try to squat with out the shoes, uexcept for front squating, If you have been squating in the shoes for a long time, your gastroc(a calf muscle) and achillies tnedon might not be flexible enough for you to get to parallel while keeping the heels planted, but going deep as you can will stretch them out.