Yes, I believe adrenal fatigue causes apathy. I had a thyroidectomy (so now hypo) and also adrenal fatigue...I feel that apathy is more due to adrenal fatigue than hypo for me. It's like I can't be bothered with anything... doing things I would normally enjoy. The fatigue doesn't help either!
I am also hypothyroid for which I take iodine. I am also suffering from adrenal fatigue, confirmed by saliva and urine tests. I take 1000 mg. of vitamin B5 daily and it has helped enormously. Ask your doctor if this is suitable for you. Also look up adrenal fatigue on the internet. This is where I found the connection with B5.
What sort of adrenal testing did you have and what sort of adrenal replacement treatment are you taking?