In any other animal, yes, the appendix produces "Cellulase", the enzyme for breaking down cellulose. However, Cellulase production in humans is either very low, or non-existent depending on certain things, like if you have an eppendix or not.
The primary method of extracting goodness from cellulose inhumans is masticatation (chewing) and the peristaltic contractions of the intestines, and the churning plus acid in the stomach.
You'll be familiar with corn-filled turds: you didn;t chew enough, and your body can't break down the tough cell walls of cellulose in the time it takes to traverse your digestive tract.
Put simply, there are NO concequences for humans who don't eat cellulose, provided you are getting enough vitamins and minerals from other sources.
Humans can survive quite handily on very weird diets. Thomas Jefferson for example, spent the last 17 years of his life eating nothing but oranges and drinking nothing but milk - as he (rightly!) knew that these two items contain everything the human body needs. Edison wasn't a food-fan - we can assume!
To answer your question, cellulose IN NO WAY aids the deigestion process. In fact, it hinders it quite severely if you eat large quantities without chewing a lot: too much blood is diverted to the digestive tract for too long, lowering the blood flow to the brain and other organs.
White bread, and in particular, white flour, do the same thing. You can't make paste with brown flour!