In brief yes they do.
Google have a massively powerful brand that very few have not heard of, simply developing the mobile OS and their applications for mobility is just another phase in their efforts to grow their empire and consumer offering.
Google’s pages are already optimised for mobile and offering a service to view these pages on is another logical step. Their investment has always been in the software and not physical hardware, and to date they have not invested in such, HTC have.
With so many services and products the platform just makes all of these a little more accessible. With so many individuals and small businesses relying on Google for their mail, calendar and task management there is no reason why the operating system will not be well received.
Google have always appeared committed to achieving their goals. Now at least 4 years into the Android project the commitment and desire to achieve is there.