things that would get screwed up are devices that use the signal to time events. some high voltage switches use these things, but overall, i bet washing machines, dish washers, computers, lights, tvs, and radios would just work.
even garage door openers should work.
clocks and larger equipment might be a bust and maybe some of the robotics stuff at plants might be a bit off, but maybe just maybe it would work. these things are designed to condition the power in most cases within a few percentage points anyways.
i bet if it's that dire, they give it a go.