If you're talking about the normal Freeview programmes delivered through the aerial, then the YouView box will work whether or not it's connected to a Home Hub. the hub is only required for the extra channels streamed over the broadband. Those obviously do need the hub.
the Home Hub doesn't have a standby button, as it's intended to be left on all the time in case you want to use it. You can program it to go into a lower power mode at night, on a timer. Go into the Hub settings http://bthomehub.home/ to enable that. Low power mode turns off the wireless, but any wired connections are still on.