Yes they do respond quickly in situations like that:I saw the result of a radio hams shack supply using a 4 mm² earth cable from the CU to shack when the PEN was lost, little balls of copper, OK with a 65Ω earth rod no problem, but the 4 mm² was bonded to the earth bar in the shack which was connected to 4 earth rods with bare copper tape between them for the radio transmitter so was better than my meter could measure, I would say less than 1Ω. He had realised there was some thing wrong, turned off main isolator to house, and called me on 2 meter as this had not stopped the earth wire melting.
It was caused by some road works, and the DNO said it was impossible, but responded very quick, and the radio ham was only person in street not to loose equipment, since he had turned off the main isolator before his wire burnt out. Why the person wiring his shack had used twin core SWA and not used the SWA as earth I don't know.
But had the supply been PME and actually had multiple earth rods it could not have happened, but TN-C-S is not always PME.
https://www.diynot.com/diy/threads/a-real-moan-tonight.552183/