Can bad posture affect how you grow as a child?

Yes: Poor posture can affect spinal development.

In short - yes: While very young child posture may be a mere reflection of any present musculoskeletal problems, the pre-teens and teenagers may have certain habits and behaviors that affect their physique. Stooping is common and leads to neck and back problems. Sitting on the floor in "reverse indian style" may lead to excessive lack of mobility of the hip joints. High heels lead to changed lordotic curvature.