73driver,
Since my key is removed when towing, the panel is not powered so the digital odometer does not indicate any mileage increase. However, in your case where you must have the ignition switch in the ACC position, your instrument panel may be powered so your odometer may add in your towed mileage. You should know if you have towed your GTI. If so, you may be able to remove a fuse to stop the odometer from indicating.
Prior to getting the GTI, I towed a 2005 Chevrolet Malibu that was also setup with a Blue Ox system. Since I was getting a new tow bar from the Blue Ox factory anyway for the GTI, I advertised the Malibu as a vehicle already setup for towing and would include the existing Blue Ox tow bar, base plate and installed tail light wiring. The Malibu had approximately 93,000 miles on the odometer when I sold it but with approximately 55,000 towed mileage that did not register on the odometer. A person drove all the way from Tennessee to Iowa to look at the car and bought it for $6,000. There is a demand for used toads.