Yes, definitely. The cortisone normally produced by the adrenal glands helps to control your blood sugar. When you adrenal glands begin to fail, your cortisone production fails and therefore you blood sugar drops. If you take cortisone or hydrocortisone it will cause your blood sugar to go up. If you are taking too much cortisone, your blood sugar will be elevated and you will be in a pre-diabetic state. If you continue taking an overdose of cortisone, then you could become a diabetic. My blood sugar was low when I was exhausted and rose when my adrenal glands began to heal.
If you are taking cortisone and your blood sugar starts to go up, check with your doctor. You may be healing and don't need to take as much cortisone. It can be a good sign.
If you are on cortisone you need to check your blood sugar frequently (at least once a week) to make sure you are not getting an overdose of your medicine.
Remember that you can have Diabetes unrelated to Addison's Disease. Ask your doctor to test and see what is happening with you.