Theoretically, you could have a very minimal hosting package or server that only stores the index.html page that is needed to access the site, you could link everything else to files stored on Google drive. I do not know if you could have the html files on Drive as well though... but if you're sharing PDF, DOC, image files and such, perhaps you could have those on Google and all the HTML on the hosting package. It would be a bit of a puzzle to keep everything organised but it could work.