Yes your liver has a very strong relationship with digestion. If your digestion becomes sluggish then your liver cannot properly eliminate the toxins and this makes you feel bad. So think of constipation being related to feeling bad and the opposite to feeling good.
For instance I ate something over the weekend not on the diet and I got constipated. I felt like crap the next day. However, all I did was support my liver and now I feel better again.