What you mean is will it bottleneck the R9 270. A bottleneck refers to the weakest part of the system, or the one holding everything else back. Therefore it would be the FX-4170 bottlenecking the R9 270, since it is holding it back.
That said, it will depend on the game and settings. It's not as simple as whether a CPU will bottleneck a GPU, because different games require different amounts of processing power and don't involve the CPU as much in rendering. Generally speaking, higher framerates are what cause noticeable CPU-bound issues along with more advanced things like shadows, lighting and ambient occlusion. Meanwhile higher resolutions, anti-aliasing and more detailed textures pretty much just increase GPU load and don't involve the CPU.
So if you're looking to play the latest games or demanding things like BF3/BF4 multiplayer with a locked 60 FPS, it's not gonna happen with the 4170. But if you're looking to play 1080P with higher settings, anti-aliasing etc. at 30-60 fps, then the FX-4170 will be fine.
Just to give you some examples, the FX-4170 would bottleneck a GTX 980 if your gameplay style was ultra settings at 1080P at 120 frames per second... but it would not bottleneck a GTX 980 if your gameplay style was 4K resolution at ultra settings at 30-60 fps.
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