In Selye's original definition the production of cortisol is stress - or the 'stress response'. The production of cortisol is an integral part of the immune response to infection. Without a cortisol response, as in Addison's disease, you are more susceptible to the effects of infection.
Corticosteroids are only relevant to dampening of the immune response if they are given in higher than physiological doses as part of treatment. Significant dampening requires more than 15mg prednisolone daily, which is probably around four times the normal level.