The new Dell 6K has kvm (and PiP) functionality across its inputs, and it does appear from my modest use of this feature so far, that it works as you would want (ie it still thinks the display is connected, even when not showing that input)
I would prefer that with 1 display but I have 2 Dell 6Ks
and it's kind of annoying if I want to have them each on a different PC. (I use a usb switch to switch my peripherals between displays)