Having to add a quart of make up oil, every 1000 miles is on the high side of what VW considers normal oil consumption, in the V-6 motor. This can be due to a few factors that you can easily rectify. From a mechanical side, replacing the PCV valve and inspecting or cleaning the associated plumbing can help reduce this rate of consumption. As you have mentioned the motor has been burning this rate of oil for some time. When a PCV valve is stuck or not performing optimally a few things can occur. Trapped unburned fuel can dilute the viscosity of the motor oil and cause consumption. These unburned fuel vapors entering the crankcase can also be the catalyst for sludge formation in the valve stem seal area. Also it is highly likely that the piston rings would become fowled with hard carbon like formation forming between the piston rings. This condition not only promotes higher level of blow by gasses but interferes with the functioning of the piston rings.
Auto-Rx will definitely dissolve the coked up deposits that form between the piston rings, which prevents proper function. ARXD will also dissolve oil related contamination in the valve train. So if I were you I would first have your PCV system evaluated for proper operation. Then I would suggest running auto-rx in the basic application mode for 2 intervals. That is clean and rinse clean and rinse. I suggest that you use Shell Rotella T oil in the 5W40 for both the cleaning and rinse intervals. I suggest finding the Shell Rotella t product available at Walley World for the cheapest price. Between servicing the PCV valve and running ARX I feel confident that you can drastically reduce the consumption levels.