I would never leave any of my digital equipment in an "on" state constantly. Shutting the device off and on again wouldn't make much difference in your electric bill, since the amperage usage is quite low.
Besides, I just feel better not having any electrical equipment running constantly, especially if I'm not home. I don't see how it could benefit the computer, either. If your concerned about not receiving updates, just set the computer to notify you that an update is ready.
Besides, it makes sense; that leaving any device on constantly will consume more electricity, however minimal that is. JMHO