On the flip side, when I had high cortisol (Cushing's disease) I had low blood pressure when it was expected to be high. I nicely retained that when my adrenals came out - so there are exceptions to every rule.
For what it's worth, I had AI at the same time as above normal BP for many months. I agree with rumpled. It is not very common. I never suffered from low BP in my life.
I am not a proponent of the fatigue school (unless diseased, our parts are designed to last a lifetime...).
There may be cases of low cortisol with higher BP - but it is not common. I have heard more of in a crisis sometimes instead of dropping, BP will oddly rise.
Testing is really the way to know if you have a true adrenal issue. Many sets of testing and a stim test.