Google has their factory image they send to their factory for their device, yes. It won't work on any other device. You can't build it from source, either. Android is not Android. The world of Android and mobile hardware is radically different from Windows and bog-standard PC hardware. Do not think the OEMs and carriers are happy with the current situation (and don't think the OEMs and channel resellers were happy with the PC/Windows situation, either). The only people who have been at all happy lately are the veritically-integrated concerns like Apple and maybe the console manufacturers. Why do you think Microsoft now has a tablet and an app store? Why do they have a games console and a walled-garden network experience?Google would beg to differ ;)
There is really no such thing as a "Google factory image."
As to the original thread of using a tablet for taking notes, yes, it can be done. You can be trained to use it for such a purpose, just as goldfish can be trained, and you can crow about it. But, just like many other simplistic demonstrations, when it comes to serious usage you'll find you need the right tool for the job. If by note taking you mean updating your Facebook status and sending tweets between looking at pictures of kittens, it's great. If you mean writing a few hundred lines of notes before looking up, you will quickly find your $700 toy is not the tool you're looking for and a $300 netbook is a better bet (and a $700 ultrabook is best). These are the prices in local money I've recently paid for these devices, your local mileage may vary.