I can speak to this from an outdoor sound technician standpoint. If we had low voltage problems, we ended up frying something. It goes back to physics Power = Current times Voltage (P = IV). The machine is going to want to boot with the needed power input. If the voltage is low due to all at once on, it will be made up with by more current to generate the needed power. I am not an electrical lineman or anything but we ruined music equipment also after a storm and the power was out for two hours or so. After it came back on, the organization wanted instant music. We powered up and ended up ruining some equipment. With that much draw on the line (air conditioners and such) the current increased in the lines.
It may be wise not to turn on all at once.