There's definitely a large number of people who only visit sites through Google's homepage. Not the address bar or anything else (clicking links being the exception).
I worked this out by hearing about customer support calls for a new URL we had which hadn't yet been indexed by Google. All the callers having problems couldn't find the address bar. They thought the Google search box was it.
Not helped by it being the same thing in some browsers. I have the opposite problem - I regularly hit the ‘.’ rather than the space bar on iOS, and then the browser thinks I’m trying to go to that site rather than search for my string (words separated by a period). It’s annoying.
I worked this out by hearing about customer support calls for a new URL we had which hadn't yet been indexed by Google. All the callers having problems couldn't find the address bar. They thought the Google search box was it.