Hm... a single 770 might be a little tough. Is it the 4GB version? I think the 770 is the lowest card that "supports" 4k, maybe the 760ti does too now that I think about it.

You will definitely be able to browse the web, play back videos, ect. Gaming at the "good" level may net you like sub 30 FPS. I recommend definitely turning off AA and ambient occlusion. You can even try and render at 75% and upscale.

Getting a second 770 would be a good bump in performance.

If you only have the 2GB version you may run out of memory extremely fast, and I wouldn't recommend playing at 4k with that.