Don't think so, I had to use a spare due to a large screw in one of my main tires and the TPMS Light on the dash did not go off when the inflated spare was placed on the X.
I had the same problem that Erick had when I was in Hawaii. I changed out the "holly" tire and put on the spare, and the light keep beaming into my eyes. It went away after I got the original tire fixed and back on.
Main tire got a nail in the sidewall. Same tire and rim as the spare so I was just going to leave the spare tire and rim on and just replace the damaged tire and use that as a spare.
So now I will just replace the damaged tire and put it back on the truck and put the spare back under the truck