The Short Version
The available evidence does not support this claim as stated. Studies show that habitual caffeine use can blunt caffeine's ability to further raise cortisol levels — but this is a different outcome from caffeine's stimulant effect on alertness, which is primarily mediated through adenosine receptor blockade. No source in the evidence pool directly measures whether pre-existing elevated cortisol reduces caffeine's wakefulness or alertness properties. The claim conflates two distinct physiological pathways, creating a materially misleading impression.