In the admin, how can you list thumbnails instead of titles for a custom post type?

I would look into adding a custom post column for that post type which shows the image you’d like to.

See this link.

edit: here’s a working example.

function add_column_header_298736( $defaults ) {
    $defaults[ 'image' ] = 'Image';

    return $defaults;
}
add_filter( 'manage_results_posts_columns', 'add_column_header_298736', 20 );

function add_column_content_298736( $column_name, $post_id ) {

    if ( $column_name == 'image' ) {
        // do stuff to retrieve your image
    }
}
add_action( 'manage_{your_post_type}_posts_custom_column', 'add_column_content_298736', 20, 2 );