Well - functioning leaves are making food for the plants. This is the food that they use to grow (fertilizer is just a mineral supplement). If you cut off the leaves then they'll have to use whatever food they have stored in the crown/roots to stay alive. Then they'll also have to use stored food to regrow new leaves so that they can start photosynthesizing again to feed themselves. Chances are it wouldn't do them any serious damage, daylilies are tough, but it likely won't help them as much as it will help you when you look at them.
