Does the parent Rigidbody compensate for children?

This is concerning 2D objects. From what I understand and experienced, having a Collider on a moving object without giving it a Rigidbody is inefficient. Also, from what I have read here, a child object with a Collider but no Rigidbody would have messages such as OnCollisionEnter2D passed to the parent if the parent has a Rigidbody. I am wondering whether having a Rigidbody on a parent would compensate for the children not having Rigidbodies on them, even though the children would move independent of the parent.