@turquoise-- Chronic constipation for a long time can definitely cause chronic fatigue. But there are other conditions that might be causing both the fatigue and the constipation.
For example, fatigue and constipation are symptoms of hypothyroidism. When the thyroid is working less than usual, it causes fatigue and it slows down the digestive system.
It kind of turns into a vicious cycle after this because both the thyroid and the constipation is adding to the fatigue.
If you have both constipation and fatigue, have your constipation treated first and see if the fatigue goes away.