Though it has been covered above, yes the vac itself plays a part in the anti-static circuit. The CT is the ground. (Earth outside the US)
My reason for commenting is actually about the usefullness of antistatic in the first place. Some say that the never see the need or point, but as soon as you touch any kind of plastic, you'll know.
Whether you are routing, sanding or sawing most plastics, especially acrylics, the moving contact builds a charge. It will be discharged, as a shock, through you. Any dust that does escape will cling to everything, since it is now charged too.