Any CPU + GPU combination can potentially be a viable match if it is well suited to the workload. The CPU does not "handle" the GPU. It "handles" the workload presented by the game engine. The GPU then "handles" the draw, the resolution, the details settings, the shading, the lighting, and the post processing. The load on the GPU is broadly adjustable, the load on the CPU is not. Increasing CPU performance is done out of necessity to meet the demands of the game engine, increasing GPU performance is done to improve visual quality. The only occasion the CPU needs to rise to is the game engine, not the GPU. Whether or not the GPU then goes underutilized, is a function of whether the visual quality (resolution, details, and post processing settings) can be turned up high enough to take advantage of the rendering performance available.
Don't ask, "can the FX-8320 handle an R9 290?" Ask, "Can the FX-8320 handle the game?"
If the CPU bottlenecks a game to an unacceptable performance level it won't matter if you're on an R7 250X with low graphical settings or an R9 290 with high graphical settings, the CPU is going to be the problem either way.
The question is then, what games do you want this machine to play and what do you consider to be a minimum acceptable FPS?
Many games will run fine on a 1.6GHZ AMD Athlon 5150, and they would run equally well whether paired with an R7 250X with low graphical settings or an R9 290 with high graphical settings. Some games demand a very high execution performance from the CPU and many demand very high execution performance available on just a few threads. Whether or not the FX-8320 can meet the demand and meet minimum expectations of FPS has absolutely nothing to do with the R9 290.
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