Yes, you may run the equipment grounding conductor within the same conduit. You may also save yourself some time and trouble by bonding your system's equipment grounding terminal to the nearest piece of building structural steel, a metallic cold water pipe or the building's electrical grounding conductor.

You don't necessarily have to follow the same path that your tie cable pairs follow. You also don't have to run the "ground" wire that far. Look for any copper cold water pipe or iron framing member (not steel studs) and you will be fine for a grounding point.

Ed Vaughn, MBSWWYPBX