I didn’t personally have it done but it’s worth an ask.
My comment back to them was it was a pretty shitty system if one tire pressure sensor malfunctioning prevented the rest of the system from working.
Basically I took a nail, swapped for the full size spare and tossed the damaged tire in the back of my uncles truck for a repair ( he runs a tire shop ). And the next day my whole TPMS stopped working. Happened to be in the dealer that week while the spare was still removed, reprogramming was the only option they had aside from re fitting the spare ( which magically made it all work again ).