Disable the built-in front-end search capabilities of WordPress.
No. This only disables WordPress's capabilities with regards to search.
The most likely cause for this is a theme that has the markup for the search form hardcoded into one or more of the theme's template files (excluding searchform.php). This is generally frowned upon nowadays (the theme should be calling
get_search_form() or using searchform.php to get the search form). There is no way for this plugin to prevent this hardcoded form from being displayed.
However, even if this is the case, the form won't work (thanks to this plugin), but it will still be displayed.