Yes, the discipline wand is used in the House of the Old.  In chapter 12, Fiona tells Jonas this.  She explains that she has a lot to learn in caring for the old, and one of the areas is "punishment for disobedience" with the discipline wand.

"[Did] you know that they use a discipline wand on the Old, the same as for small children?"

She does not go on to elaborate, but we can assume that since she says "the same" that the application is the same.  In chapter 7, the discipline wands are described as “a system of regulated smacks” with the discipline wand, described as “a thin, flexible weapon that stung painfully when it was wielded” and the Childcare workers are specially trained to administer “a quick smack across the back of the hands for minor misbehavior” and “three sharper smacks on the bare legs for a second offense.”

Note that this system is only used on small children.  Older children make apologies for misbehavior.  The fact that the community treats the Old the same as young children implies that they do not consider the old to be adults with adult rights and characteristics.  They are considered dependent, like small children.