Honestly speaking, I don't like the word "carputer" myself ... it sounds so abrupt and so technically improvised.
Since this is going to be a custom built machine for this specific car, surely we can coin a nice special word for it ... I know you are great at suggesting names ... so I think you should have the honour to select a name ....
TPMS is already there in the car ... Surely it is possible to incorporate TPMS in the computer but that would involve installation of programmable sensors, programming kit and extra hardware in the computer.
With reference to the VIPER thread discussion, that is a different case. You want a 2-DIN solution computer solution for everything without the clutter and glitches and pitfalls ... so perhaps you can look for the possibility of hooking up TPMS sensors, but to my mind, spending 12500 on a TPMS separately would be better than going for something which might not work .. or is expensive than other solutions.