Well yes, but I'd rather play at 1920x1080 and not have to sell a kidney for a graphics card that can drive the 4K display.
You still have that option, I can't imagine any 4k displays would fail to support running at a 2x multiplier given that it is designed specifically for that.
The next generation of graphics card will probably be able to take the dubious honor of being able to run Crysis (2007) at 1920x1080 / 60fps on a single GPU...