So I highly doubt it but just to clarify with more intelligent people, the rx460 won't be bottlenecked by the I3 4160
The RX 460 cant be bottlenecked by an i7-7700K.
Pick a CPU that meets your performance goals in the games you want to play.
Pick a GPU that meets your visual quality goals at the resolution and performance goal in the games you want to play.
Don't think that by preventing bottlenecks through ideal component pairing you can get more than the sum of parts. The performance of the i3 in gaming will be the same whether paired with a low end GPU or high end GPU. If your performance goal is above what the CPU can deliver, you'll bottleneck any GPU trying to get to your performance goal.
Bottlenecking all depends on the game and graphical settings and any CPU can bottleneck any GPU under the right circumstances. Bottlenecking is not a absolute thing or a yes or no thing like it is made out to be.
Also it is 100% meaningless to even think about provided you chose your parts right and get what you want. You should chose the CPU for the FPS you want and the GPU(s) for the graphical performance you want. If you are happy with what you get and meet your goals when why worry about something that is not effecting you?
Farther info: https://pcpartpicker.com/forums/topic/214851-on-cpugpu-bottlenecking-in-games
This focuses on gaming (which is what you're likely doing with that combo) but many of the same concepts still apply elsewhere.
Look, can we just add a feature to the site so that when a user with an account less than 30 days old tries to create a thread with the word "bottleneck" in it it immediately redirects them to that post?
Kinda, but not by enough to worry about. In general, it's a good GPU but not powerful enough to show a large difference in FPS among CPUs.