How bad is it for my A/C unit if I cut the power while it's working?
You will need to protect against short cycling the air conditioner

When you turn an air conditioner compressor off, the pressure in the system does not equalize instantly -- instead, it takes a few minutes for the pressure built up on the high side of the refrigerant circuit to equalize with the pressure on the low side.

If you turn the compressor back on before then, this is a problem because now the compressor is trying to pump refrigerant into a zone that's already at high pressure, which puts quite a bit of stress on the compressor.

As a result, your device will need to delay a few minutes (3-5 is typical) before allowing the air conditioner to turn back on after it shuts it off.