It is possible by setting $config['enable_query_strings'] = TRUE; in your config.php file (As DamienL answered). I just tried with a fresh CodeIgniter installation from here.

However, it appears there must be at least 2 variables (separated with a "&") for it to work.

Here are the steps I took to make this happen:

In config.php, I changed $config['base_url'] to the appropriate directory and set $config['enable_query_strings'] = TRUE;

In the controllers directory I created the following class:

class Testing extends Controller {

    function Testing()
    {
        parent::Controller();   
    }

    function index()
    {
        $this->load->view('welcome_message');
    }
}

/* End of file testing.php */

/* Location: ./system/application/controllers/testing.php */

I can then access the index function with a query string, but only if there are 2 or more variables like this:

localhost/CodeIgniter_1.7-1.2/index.php/testing/index?id=123&cat=abc

If you absolutely need both the segment-based and query string-based approaches, but only need one variable in a particular query string, I suppose you could add a second "dummy" variable and just ignore it.