If it's a sky+ box then i don't think so, mine went off in a power cut and it stopped the hard drive from working. but you should be fine with a standard box.
They advise you to keep it on sandby as much of the time as you can, which I've only just found out because apparently it increases the life of the box. It might help to call Sky and ask them.
I always left mine on, or on standby so it would continue to record my series links. If it's on standby the programs will record as normal - there just won't be anything on screen.
sorry meant to say - if you have a power cut as mntioned - you lose your pogramms. if you unplug it - which is switching the box off - you can't record anything - which is why standby does oth. Hope this helps