Should I pass the $form parameter when building system_settings_form?
The form parameter is passed from drupal_get_form(), but if you choose to start a new form array it doesn't really matter. The form works as expected.

However, it's good practice I think to include $form and $form_state in the parameter list because if you ever change your menu entry to pass an argument, then all you need to do in your form builder callback is to add it to the list at the end.