Would these "average people" try to press Ctrl+F? If the argument is that most of the public is ignorant to the client-side jumping/highlighting facilitated by Ctrl+F, what purpose does overriding Ctrl+F serve? It seems that people who press Ctrl+F would have an expectation of what should happen next, and people who want custom search would move their mouse to the search bar and click.

Maybe a better compromise would be including a modal or a hint highlighting the site-wide search box without suppressing the native Ctrl+F functionality.