Yes, it will, so let’s do the math.
1920 x 1200 x 4 = 9,216,000 bytes per frame
* 60 Hz = 552,960,000 bytes per second
/ 1024 / 1024 = 527.34375 MiB per second
1x PCIe 1.0 lane runs at 250MiB/s * 8 = 2000MiB per second
1x PCIe 2.0 lane runs at 500MiB/s * 8 = 4000MiB per second
1x PCIe 3.0 lane runs at 985MiB/s * 8 = 7880MiB per second
And that’s only on 8 lanes, most people are running 16, you have a ton of headroom before it becomes an issue.
Let’s assume 16 lanes of PCIe 3 at 15,760 MiB per second and calculate the teoretical maximum at 1920 x 1200 and 4K
16,525,557,760 / (1920 * 1200 * 4) = 1793.14 Hz
16,525,557,760 / (3840 * 2160 * 4) = 498.09 Hz
Games do need much of this bandwidth, but only when they launch and are loading their textures for the first time, so there will be a performance hit but it will be marginal. In fact my TimeSpy score drops about 100 points when I am using the program, but in general gameplay it is undetectable. Also my 1080Ti is only on four lanes (AB350 Pro4 only has 4 lanes on the 2nd PCIe slot), so my score may be improved if it was in a 16x slot.
If this in the future ever doesn become a problem we can look at using the YUV420 color space which is native in hardware (so fast) but consumes only 12bits per pixel instead of 32, but at the cost of color accuracy. See other streaming services (Steam/ShadowPlay) for what that looks like