I'm not sure I am entirely clear what you're asking. Do you want to pair only the G3220 CPU with the 7790 GPU, or are you hoping to use the integrated video of the CPU with the GPU in games, or just use both graphics devices for a multi-monitor configuration in desktop usage?
The processor and GPU you have selected will pair perfectly fine. You will not be able to combine the CPU's built-in graphics with the HD 7790 for use in games, but you should have no problems using both to drive screens for a multi-monitor setup for use with Windows Desktop.
As for bottlenecking Battlefield 4 with that CPU, the game itself is CPU bound, but only when you have a fast enough graphics card. I suspect your bottleneck with your combination will be the graphics card you have chosen. If you look at the graph that was linked to, the difference in performance in processors between what you've picked and what's possible, is practically indistinguishable, and that is when removing most of the GPU's bottleneck.