Adrenal fatigue is when your adrenal gland craps out and stops producing adrenal steroids like DHEA and Pregnenolone. This leads to decreases in testosterone, estrogen, and cortisol. Cortisol levels will get up there, but it takes a long time, which is why people usually feel at their best when the day is almost over, just takes so long for cortisol levels to build up over the day. Ultimately, you will have low cortisol when you want it high, and high cortisol when you want it to be low.
In the case of a cortisol inhibitor, we are not shutting down cortisol production entirely, but rather tweaking it as to reap the benefits of lower cortisol, without going so low as to see the negatives. Provided you don't have adrenal fatigue, you'll still have high enough cortisol levels during the part of the day when they need to be high, but simply not as high as to cause more utilization of muscle protein for energy and deposition of fats.
You bring up a good point though, and for the reasons you mention (symptoms akin to adrenal fatigue), LeanFX is not a product you want to be mega-dosing in hopes to lose more weight.