Is there an official Android "Google" ROM?
To answer if Google distributes binaries for your device: No, they do not (Unless you have a Nexus device). They do, however, have the full Android source code available so that if you wanted you could compile the source code for your device. However, that leads into your second question about the drivers and such. Yes, you will need to find the drivers and any other proprietary files that your device requires for it to interface with Android. You would have to search about compiling a custom ROM for your device and how to include these files. 

Likely, your simplest choice is find an AOSP (Android Open Source Project) ROM that exists for your device and install that. Check the XDA Forums to see if your device is included on their site. IF so, go into the development sub-section for your device to search for ROMs.