Nope... by license agreement the console would have to work with out mains power or a HDTV via mains natively by design....
The Consoles (all of them not just PS4) Is built as a IN place mains activated device with "TV from sky" HD enabled service..
Skygo is in the name, skygo is MOBILE the devices are NOT connected to mains power or wifi or cell network all the time...
So when you pick up those devices they work with out a power cable due to built in screens and batteries... but are only SD content only still..
The Production and licensing companies only allow it for mobile devices... and a mains powered HDMI connected device is not a mobile device...
Windows/Mac Oses run on Tablets and laptops... TV from Sky is not avalable on mobiles...
Will that change, Do not expect it to, the other media apps on the console don't allow downloads for zero day HD ondemand content for the same reason...
A hand held console Would not be licensed to TV from sky but instead would get sky go, the replacement for the PS vita gets SkyGo and a brand new development company to make games for it... aka the Z5...