It is possible to method to overwrite the default search function in wordpress? I've attempted while using filters, however they only allow contributing to the query... or even spinning the entire query using posts_request. Basically overwrite that though, not one other querys works. I've the next code

function my_posts_request_filter($input)
{
    if ( is_search() && isset($_GET['s'])) {
        global $wpdb;
    }
    return $input;
}

add_filter('posts_request','my_posts_request_filter');

I possibly could override $input with my custom SQL, but there's a widget around the page which shows recent posts which wouldn't show basically do that. It is possible to method to JUST overwrite the search function??

This is not bulletproof, but presuming the very first WP_Query call is perfect for the search request (there might be considered a scenario in which a wordpress plugin calls it before WordPress does, but it's unlikely), you are able to strip the filter when the function runs.

function my_posts_request_filter($input)
{
    if ( is_search() && isset($_GET['s'])) {
        global $wpdb;

        // do your funky SQL

        remove_filter('posts_request','my_posts_request_filter');
    }
    return $input;
}