Cannot get rules component to fire on Commerce Completing the checkout process
It's possible the user doesn't have access to execute the rules component. You can check the permission in admin user permissions or on the rule component edit page.

Keep in mind the rules component will need to be attached to a reaction rule to fire on the checkout complete event.

Other than that, if the component can process the passed $commerce_order parameter (passed to checkout complete), then it should be ok.