The hits algorithm itself is only a high level description of what goes on, there is alot more to actually implementing a search algorithm that can accurately span the content of the web.
Standard (meaning off the shelf) relational databases won't work because they don't store and index properly. They won't work as a low level store because they can't find and read information fast enough, so you can't build an engine on top of it that spans the
WWW.
You COULD build your own relational database that has the low level design that can access the large amounts of information in less then a second and interact it with it through an SQL query engine. But it would be somewhat pointless.
SQL is a sledgehammer when it comes to the relatively repetitive accesses google has to perform to complete a search.