I believe any pharmaeitucal we put inside out bodies has direct effect on our endocrine systems. Something as simple as Vitamin C, sugar, or a cigarette does, so heavy duty hormones will definitely imo, this is partly why ASI tests are inaccurate, they can change from day to day. I did a test once, one test on a day i spent at home - LOW cortisol, the next day I did excercise and shopping - High cortisol. Its more about the hormone balancing rather than cortisol being the sole culprit...to much emphasis on it, but its a good starting block to getting sorted.
I know my endocrinologist wanted me off Isocort and glandulars for six months before doing ACTH stimulation tests, I dont know if you have to be that drastic, but you are taking hormones, and they cant definitely disturb the homeostatus of the body for a long time