I would certainly think that the TPMS system (if it is faulty) would be covered under warranty.
We had our first experience with TPMS this week. The nominal pressures (cold) are 36 PSI front an back. I set them up properly, and ran the TPMS calibration around 2 months ago. This week the TPMS warning came on. The tire pressures were 32, 32, 34, 36. That does seem like reasonable sensitivity. I filled them all to 37 and ran a TPMS calibration and it is fine again. Keep in mind that the TPMS calibration process is not immediate. I think the manual states it can take up to 30 minutes of driving to complete.
It is a little weird that the system doesn't actually measure pressure. It counts wheel revolutions, and assumes if a wheel has more revolutions than the others over a period of time that the pressure must be low. This seems like an OK method, but I would prefer if the system reported which tire(s) were responsible for the warning. If you get a TPMS warning, all you can do is check, and re-establish the correct pressure in all 4 tires. I suppose this enforces good maintenance practice because most people (myself included) do not check tire pressures often enough.