If you try to control the air-conditioner just by cutting the current and restoring it, which is essentially the same as pulling the plug out of the wall, you may find that doing this frequently will eventually damage the air conditioner, just as frequent power outages can. It just depends on what cycle the air-conditioners in when the power is cut/restored. So that’s not usually the recommended method.
There are a number of different ways to make an existing air-conditioner smart so that you can turn it on and off gracefully. It just depends on the specific model.
If the air-conditioner already has a remote control, then you are much more likely to be able to make it smart in this way. There are a number of different devices that can do this, but it depends on whether your remote is IR or a radio frequency and the specific device. Different remotes will work with different smart options.
There are also “robot fingers“ that can be used to literally push the buttons on the unit, but that method can get expensive.
I have owned the Frigidaire Wi-Fi air conditioner which works with Alexa, and it has been very reliable and useful for two years now. I can’t speak to any other models, but I’m happy with mine. ( i’m quadriparetic, so I can’t use the handheld remote that came with it.)
You can go ahead with your plan of just plugging it into a smart Outlet, but you might want to check with the air-conditioner manufacturer and see what they recommend and if it can handle that many power outages.
But as far as the rule complexity you describe, yes, that can be done with SmartThings, although you may have to use custom code to accomplish it.