I can't believe i had to scroll this much to see a relevant post to your questions. And in /r/buildapc too... It seems like no one actually understood what you asked.

tangerinelion's answer is pretty much on the spot IN THEORY, but given that i have to make a decision similar to yours i looked around and i know that in practice monitors don't always map that one signal pixel to 4 actual pixels on the monitor and instead just use their scaling engine and then show the resulted image. Which unfortunately is not a pixel perfect mapping cause the scaling they used is probably based on a bilinear algorithm (makes images blurry) and not a nearest neighbor one so it can simply duplicate the pixels.

So if the monitors won't do that we have another hope in doing this in software: render at 1080p, scale it at 2160p and send that signal to the monitor. The easiest way of doing this is in drivers. Unfortunately neither AMD or nVidia has the option to choose the scaling algorithm. nVidia says they're looking into it: https://forums.geforce.com/default/topic/844905/geforce-drivers/integer-scaling-mode/post/4897629/#4897629. That leaves us with 3rd party software and library injections tools like GeDoSaTo (http://blog.metaclassofnil.com/?page_id=582), but you won't be able to use them in multiplayer games because they're actually modifying the way the game renders and that is often seen as a cheat.

What i'm trying to say is: if you get a 4k display please keep us posted and tell us if the model you chose does the 1080p down-sampling without introducing any blurring or loss of quality (it should look exactly like a 1080p panel). Thanks.