More likely that they'd go to rolling brownouts of complete circuits. If the grid is that close to capacity, a handful of KW's here and there won't help. They'd have to write programs to turn off tons of meters all at once. And then since many AMI systems are on some kind of meter to meter mesh network with radio comms back to the utility, the guarantee that a meter would always get the shut off signal when it's desperately needed isn't really high enough.
They'd likely just implement SCADA controls to shut off whole circuits at once, and then rotate the outages around if it was an extended capacity situation.
They'd possibly look to implement some islanding procedures as well.
Shutting off meters 1 by 1 just isn't as efficient. Much less moving past the meter to a thermostat level where individual loads in the house could be shut off.