Found out that the Audi Q5 (probably others) doesn't use wireless TPMS transmitters mounted to the wheels, but rather uses the same type of system we had in a Ford Freestar 5 years ago. Basically it uses the ABS brake sensors to measure the overall rolling diameter of the wheel/tire combination and warn of any consistent deviations outside a certain margin which would indicate that the tire is losing pressure. As with the Freestar, there might be a need to recalibrate the system when I mount my winter wheels and tires if there's a significant enough difference in overall diameter. There shouldn't be, since the 235/65-17s that I chose are almost exactly the equivalent fitment to the OE 235/60-18s.
The upshot is that I don't need to buy extra TPMS sending units for my winter wheel & tire package which 1010tires is shipping this week.
Yipee!