No, not unless they get moldy or something, but if they are just dying I leave them. From what I've read they hold nutrients and use up the nutrients until the entire leave is shriveled (if they are dying).
If you can lightly tap it with your finger and it falls off then it's ready to go.
If you're growing a mother plant, most people cut all but the very bottom and very top most (top 2 or 3 sets) fan leaves to promote lower growth by providing more light.