|At 4K, a GTX 980 can run Battlefield 4 at Max settings at around 61 FPS average:|
There are several other benchmarks on there too. For example, Metro LL with similar settings runs at around 29 FPS.
I would assume you'd get even better performance on the 144 Hz monitor, considering 4K is 4x as many pixels as 1080p @ 60 Hz, yet 144 Hz is only 2.4 times the data being sent.
If all you use is one screen at a time, then yes, you will be able to run it fine.
User Info Page Biography for full specs.