Possibly. Physical stress - yes. Normally, the adrenal glands make higher levels of cortisol when someone is seriously ill or injured, or recovering from surgery. Since a person with adrenal insufficiency can't do this, the gap between how much cortisol is needed and how much is available widens, and can lead to adrenal crisis and life-threatening shock if they don't receive "stress doses" of steroids.
Possibly. Emotional stress - very unlikely. Everyone experiences stress on a daily basis. Even a severe stress such as the death of a family member, that can certainly cause physical symptoms like insomnia, poor appetite, heart racing, and shakiness would not result in an episode of adrenal crisis unless there were other physical stressors present as well.