I don't think its the shutdown that's the problem but the restart. If I fiddle with the thermostat on my fridge, it turns off in one direction, but if I turn it all the opposite way it won't come back on for a few minutes. I think this is the relevant interlock. Something about letting pressure equalize.

The wiring diagram for this article seems to reflect it would be a hard shutdown. Most HVAC systems I have interacted with have zero problems with a sudden power loss. The only potential issue is bringing the compressor back up too quickly on the other side. You could easily control for this if you were switching the whole unit using software.