Maybe sometimes it will, it depends heavily on the game and your settings. I will point out that CPU workloads are generally the same regardless of your resolution & detail settings, so you're more likely to find a bottleneck at lower settings. The stress on your GPUs at 4K will probably hide any CPU issues that you might have had otherwise.
As an aside, your CPU is nearly 4 years old. You're definitely in "upgrade territory" if you have the money to do so. If you don't, don't worry about it, its still not terrible.