Will my Xbox One still work if I unplug the HDMI cable?
Solution 1:
You are actually able to turn the Xbox One off. If you hold down the home button, and choose turn off console, as long as the white light on the power box is on, so is your Xbox. Downloads will continue.
Solution 2:
Removing your HDMi cable does not affect the download at all. I don't even think the Xbox knows that the cable is being unplugged.
So unplugging your HDMI cable is safe. The same goes for any cable other than the internet cable or power cable.