Not by the connections, but from the benchmarks I've seen GPUs can't keep up with that for graphics-intensive games. FreeSync/G-Sync do help a bit getting at least more than 60 fps.
I see this said all the time and it is extremely silly. Just because there are new games that don't run at 120Hz and 4k with the highest settings on a recent card doesn't mean that "GPUs can't do 120Hz at 4k". Graphics settings, more GPUs, games that are just a few years old, and anything not game related still apply. Saying "GPUs can't do 120Hz at 4k" is nonsense.
E.g. here's benchmark numbers delivered by Nvidia, and even their best card doesn't hit 120 fps in all games at 4k - if you want fps over resolution, you're going to switch down, especially if you aren't on a truly top-of-line card. https://videocardz.com/77983/nvidia-geforce-rtx-2080-ti-and-...
These benchmarks are conducted on the games "ultra" settings, which most of the time forgo any idea of resource efficiency. Games are highly configurable and often give the options to increase framerate a lot at a negligible visual impact, even just lowering the preset to "high" achieves this most of the time.
Also, with variable refresh rate, reaching exactly the maximum refresh rate of the monitor isn't very important.
The comment chain also referred to reaching "more than 60 frames on higher than 1080p resolution", there are luckily more options than 4K.