If I switch the TPMA from my existing wheels to a new set of wheels, will my car recognize them and read the tires air pressure or do I have to reset the cars computer somehow?

 

I think that the PCM3 will see them and learn from them.

 

That should work fine but how old are your current sensors... they typically go out due to battery drain after 4 yrs. May be better to install a new set of sensors depending on how many months are left on the original sensors.

 

I just put a new set of Porsche winter wheels and Pirelli tires on my 2010 C4S and you get a yellow warning light on dash first.

Through the TPMS function Reset to new tires and system "learned" and then displayed tire pressure.