Probably half the clocks here run on battery power. Not sure if my enlarger timer runs off line frequency or not, but having worked in a power station years ago, I can assure you that while there may be drifts over a long period, there won't be sudden changes. Connecting an alternator onto the grid that hasn't been perfectly synchronized in frequency and phase results in loud rumbling, shaking buildings and a circuit breaker the size of a house tripping out!
It's interesting to contemplate -- not too far from here is the Ephrata Cloister, home of a very strict religious sect in the 18th century. They had clocks -- but only with an hour hand -- minute precision was considered unnecessary.