Basically, yes, your CPU is more of a limiting factor than something like a good i5 would be. However, if it is not limiting your current performance so much that it bothers you or is even a noticeable problem, then upgrading your graphics card will not cause it to be more of a limiting factor assuming you are trying to get better picture quality, not higher FPS.
People blow this "you need CPU X for graphics card Y" thing way out of proportion. Ok, you have your CPU and it is at 4.0GHz. Does it feel sluggish when playing games? Upgrading the graphics card will not, and I can't stress this enough, NOT lower your performance.
If you have a Pentium G3280 at stock, 3.2GHz, with a GTX 750 Ti and you upgrade to GTX Titan X SLI, then performance will not drop. Some games might not get any more performance out of it because the CPU is holding that back, however, you will be able to go from 720p medium to high settings up to 1440p maxed out settings without hurting your performance much at all.
So let's say you have a GTX 750 Ti and a Pentium G3280 at stock. You play CS:GO at 720p with high settings and get around 45FPS (just pulling numbers around).
So, you upgrade to a GTX 970. Because of the CPU, your FPS didn't really increase much. Now it's 50FPS. However, now you can raise the settings to maxed out at 1080p and your FPS is now around 40FPS.
Let's say you have an i5-4670K overclocked all the way to 4.6GHz and a GTX 750 Ti. In the same medium settings and 720p, you get 60FPS. Upgrading to the GTX 970 and keeping those settings, you get a huge increase- Let's say it's not 100FPS. But, now you raise the settings to maxed out 1080p and get 45FPS.
In the first example, we see that the G3280 isn't really capable of more than 45FPS to 50FPS, but the i5-4670K is capable of much more when the graphics card is more powerful and you don't raise the settings. However, if you raise the settings, then your FPS will be limited most by the graphics card again and the i5 simply isn't being loaded up because the GPU is getting slammed.
Does this help?
Point is, if the performance you are getting on your FX-6300 at 4GHz is satisfactory, then you can upgrade the graphics card and raise the quality to get a better quality picture without making the CPU much more of a limiting factor.