If Google will bring Android apps to traditional desktops they can gain something in a short run, but hurt Android as a platform replacing Windows. Android as Windows replacement can bring Google much more, but it would take much more time.
Personally I hope that Android with or without Google will replace Windows.
Android has potential to be next Windows, because it's getting commoditized right now. Thanks to cheap devices. Apple doesn't have that, because it doesn't want it.
I think there are few things remaining for Android to replace Windows (in no particular order):
1. UX - what you already said.
2. Cheap and universal docks for even cheapest devices. Alternatively cheap wireless display technology (without lags), something more than ChromeCast - again even for cheapest devices.
What can be used for this? Bluetooth (sound and input) and/or USB-OTG (with charging of device).
3. Android needs to be selfhosting - you can't rely on Windows or traditional desktop linux if you want to replace them. There is toybox and Aborginal Linux project from Rob Landley on http://landley.net/ Recent commits advancing in the goal of building Linux kernel with clang will come in handy too.
I think that all of these will eventually come, but ask myself is this what Google really wants now.
ChromeOS seems more in line with Google business model.
They are using NaCl to bring Android apps to ChromeOS, so probably it could enable Android apps for Windows. But that would undermine Android as replacement of Windows just like Wine for Desktop Linux.
Personally I hope that Android with or without Google will replace Windows.