There are so many people with Addison's on forums that complain about morning nausea and/or fatigue. It also seems that they wait a while after waking to take their hydrocortisone.
You may not be a morning person, you may never be. Taking your hydrocortisone before getting out of bed can make your transition to waking up and getting out of bed much easier.
Here's what you can try, get an alarm clock with two alarms (some cell phones have multiple alarms, excellent for reminding one to take meds). Set one alarm thirty minutes to sixty minutes before you actually want to get up. The night before, put your pills in a small cup, put a water bottle next to your bed and if you don't feel like you can take meds without food, put crackers with the water bottle and pills. When your first alarm goes off, take the pills. When the second alarm goes off, get up.
I'm not exactly sure why some people subject themselves to waking up with nearly no cortisol in their bodies. It takes about 20 minutes for hydrocortisone to get into the bloodstream when you take it orally. That's a long time to wait for the meds to get into your system. Why feel crappy for one + hour out of your day??
Try it, you might like it.