Where can one find referenceable stats or industry research which highlights the percentage of users who search vs. browse on consumer web sites. Are there any known studies in this area?
I think you are going to be hard pressed to find many such studies because they are both very valid use cases that can, and should, live side by side. For example, if I am looking to purchase a snowboard I may go to a commerce website and browse their snowboards section. Alternately, if I am looking for a snowboard with the picture of a yeti on it I may search for "yeti snowboard" or something along those lines.
Both search and browse should live harmoniously for your users to be able to use a website and accomplish anything. Obviously often sites do alright without implementing search and just depend on Google to get users to appropriate pages.
This article dives straight into the topic and goes to say that a study by AGConsult found that often less then 5% of users actually use the search on a website. They do also reiterate that it is an important component to have, and that it shouldn't be dismissed.
50% of user are so-called search-dominant according to a study conducted by Jakob Nielsen. Those 50% will prefer a search field over menus. He recommends that if your site contains more than 200 pages you must add search.