No, voltage can be dropped a bit. "Brownouts" are a thing. But they're less effective than they used to be, because everything with a switching power supply will draw more current if the input voltage drops. That's now a big fraction of the load.
Surely it’s not a big fraction of the load tonight. This whole problem is being caused by heaters.
But heaters on thermostats will just run more if they are putting out less wattage. So across your whole population of houses, you won't move that part of demand much (maybe a few were already running at 100% duty cycle).