I'm ordering a wheel/tire and it's $31 for a stem and TPMS monitor. Tire Rack notes that dealers may be reluctant to install a wheel without TPMS. Sure I can mount it myself, but if I call AAA or somehow end up in a shop with a bad tire, it could get complicated. My main concern is, does having a dormant TPMS in the spare have any effect on the system in the car? Are they motion activated?
Get a TPMS sensor for your spare. I've done it and have had no problems or interference with the tires mounted on the car.
I ordered a full size matching 20 inch wheel from Ford when I needed to buy new tires. I took the best tire, left it on the existing wheel and with the original factory TPMS unit, and put it in the trunk for a spare. I had Costco mount the new tires on the other three remaining existing wheels, and add a TPMS unit to the new ford wheel when they mounted the tire. They set (relearned) the TPMS units for each tire and wheel on the car and the TPMS unit in the trunk on the spare was ignored by the car's computer. The spare with a TPMS sensor didn't interfere with the operation of the TPMS units of those mounted on the car.
Shortly after my new set of tires, I had a puncture in the side wall of a tire due to a road hazard. I mounted the spare, went back to Costco. I had to leave the blown tire while they ordered a new tire (for $1.00 prorated under the road hazard warranty). I also had them turn on the mounted spare TPMS unit. It worked without any problems.
My guess is that each TPMS unit has a different serial number associated with it, and the computer read only the serial numbers it has been relearned to read.
The spare air pressure should be checked occasionally, since the system only reads four TPMS units and not the the fifth one.