At least in my area they can. I have an agreement with the power company that they can shut off my A/C for up to, IIRC, 10 minutes at a time with some maximum total time off per day to load shed in times of high load. In return I get a discount on power during the summer months.
Except for the first year where there was a bug that turned it off for an hour at a time, it's never been noticeable.