The CyBook is a computer. The screen doesn't use any power when it's simply displaying a static image but, just like any other computer, the other parts of it - the CPU, the RAM, etc - certainly use power.
You can leave it permanently switched on if you wish, certainly. A battery charge will last about 4-5 days if you do so, as opposed to (probably) several weeks if you read a couple of hours a day and switch it off after every reading session. It's entirely your choice.