Nick,
To do that, you'd actually have to edit the com_users template file for the login page. That's where users are automatically redirected when their session expires.
The best way to make the edits is to copy /components/com_users/views/login/tmpl/default_login.php to /templates/<YOUR_TEMPLATE>/com_users/login/default_login.php (create any directories in that path that don't exist). Then, edit that file there, basically removing just about all of the code.
Copying the file creates a template overrides so that your changes won't be lost if you update Joomla in the future.
I hope that helps, but if you need anything else, just let us know.
Thanks,
Alex