Even the "hd graphics" or low end Kaveri GPUs from AMD can drive 4k.
Hell, Adreno from Qualcomm can probably drive 4k.
Desktops, compositing, and light effects like transparency are nothing next to video game or 3d model rendering. In practice, any GPU manufactured today is enough for non-3d purposes, unless you try running 3 4k monitors off the numberless hd graphics or something.
If you aren't getting 60 fps scrolling, it is usually due to the cpus being low powered and the application not using GL accelerated drawing for the scrolling.