So, I can't speak for the Yamaha receiver until I look at the manual, but I know that with decent Denon receivers, you can actually setup HDMI pass through when the receiver is off. That is, when you power off your A/V receiver, it will pass HDMI audio and video through it directly to the TV.
This is great for things like (most notably) cable television. Where your wife/kids just want to turn on the TV with the TV remote and watch... TV. They don't need to turn on the A/V receiver or switch inputs. You don't need to use ARC or a different HDMI connection on the television to watch cable, you just power the TV on, use the TV remote to adjust volume, etc. On Denon receivers, you can select what source you want passed to the TV when the receiver is powered off. You can force it to use a specific source, like your cable tuner, or you can tell it to use the 'last used' source. So, if you used your Blu-ray player last, it will select that as the source. Best part, is that the choice is yours.
Sure enough, page 120 of the Yamaha manual indicates that same type of functionality.
Yamaha calls it 'Standby Through'.
https://uk.yamaha.com/files/download/other_assets/8/799468/RX-A1060_Manual_English.pdf
So, go ahead and hook that cable box up to the A/V receiver as well, and it will playback through the television just fine while the receiver is powered off.