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.
This is almost certainly not a capability of your meter as such, though the meter might be used to pass data back and forth. Either your thermostat is being controlled (i.e., via changing setpoints) or there's a device somewhere in your HVAC wiring that the utility can communicate with. What is for sure not happening is remote connect/disconnect in the meter used to shed load.
Correct! I didn't think it was worthwhile making the distinction but there's a separate interface that the power company can control that switches the A/C. I think (been a while since I paid attention to it) that it only controls the compressor: the blower is still allowed to run independently.
I worked with a power company in New Zealand that had load shedding like this (although more for water heaters IIRC). They transmitted signals on the power lines themselves at a much higher frequency than the AC delivery. The end devices also needed to support it.
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.