Household wrapping won't do any good when you place it inside walls. This can only cause your walls to accumulate water or moisture inside and not allow it to escape. Since you want to prevent water from entering inside rather than outside, doing so is not useful. Although some wall coverings might have it below the floor, a day ago.
In your case, the wrapping in the cavity is definitely a good idea. In addition to sealing the coating a little with air leaks, it will prevent liquid water from entering the insulation. Wrinkled wrapping is also a good idea. Technically, household wrapping is a type of water resistant barrier, or WRB.
The purpose of using a household wrap is to prevent moisture from entering the wall cavity from outside. While home wrap is water resistant, it's generally not waterproof or waterproof, for good reason. Just as rain and humid air can enter a wall cavity from outside the house, moisture-laden air can also enter a wall from inside the house. If a household wrap is waterproof, it can trap this interior moisture in the wall cavity, which could cause rotting and mold growth.
Most WRBs have a permeability index between 5 and 60; most building codes require a minimum of 5.