I just got a pearl and installed it.
The good news, it is dumb enough (unlike the nest) to believe me if I say there is an AC. It comes defaulted assuming there is one. You can also change the setting on the device.
So it looks like I will be able to use it to control the window AC.
It didn't work at first linked to google home with the generic driver. But I found that either the Zen or the Lux Zigbee drivers worked. The generic controlled the device, but wouldn't accept commands from google home.
Suggestion for others - I went with white, as it would match switches etc, but it looks a little weird. With no C wire, the screen is fully black inside a white frame (I heard it might show temperature with a c wire). I'm not a huge fan of the look, but for $80 I'm ok with it - plus couldn't find a black one. The nest was definitely prettier.
EDIT: I take it back, those 2 drivers (zen and luz) work to control the device from google home, but apparently don't report back the correct battery level or status (heating/cooling/idle). So I changed back to the generic, and now it is working with google home. Hopefully it stays working - best guess maybe when I resynced devices with the other drivers google home figured it out, then switching the driver back works? Or maybe I just got it all wrong in the first place!