The only thing TPMs is for is to notify you when tire pressure drops below a certain point (usually.24-28psi). On some vehicles the sensors will relay each tires pressure to the driver via the DIC. On others such as our Sonic the only notification we get is a Dummy light when a tire is low.
Onstar also monitors your TPMS readings, they also get the actual pressure relayed to them as well. As I'm sure anyone that has seen the onstar reports or looked at the app already knows this.
Removing the sensors will only illuminate the light on the dash. Not sure if there are any legal ramifications by running rims with the tpms removed. I doubt it but not sure.
As for putting a sensor in the spare, that will do nothing for most cars. If the car was not equiped with a sensor for the spare then it will not recognize one has been added. When I was working on cars I never came across a model that could have the computet enabled for this sort of add-on. Each sensor has its own sort of IP address that is transmitted to a reciever (along with psi), this allows the comp to determine where the wheel is at and also why the system must be "relearned" after a tire rotate, while all the psi will be accurate the computer will still thing the tires are in the same place (eg. If the RR is actually low it will report the LF is low as that was its last learned position). This is alos why adding a spare tire TPMS will not do anything, the comp does not acknoldge an additional transmitter. There may be a car that may be programmed to accept a 5th transmitter but I am unaware of any at this point.
Sorry for the wall post but there is some of what I know on the subject of TPMS and I hope it helps
-tyler