Well, allow me to frank, they both are not perfect match, because bus, PCI-E x16 2.0, provding by AMD FX-6300 could not satisfy the most idealised bandwidth which RX470 needs. But RX470 is a strong and high-end (cost not that few) GPU, it can still level up your system. I would recommend that you upgrade your platform to AMD Ryzen, if possible, wait for some time, buy the next generation of AMD GPU.
Yes they will work together just fine, for most games you should be able to play at 1080p high settings and get a stable 60 just fine, very high or ultra might be a stretch though.
And FYI the 5GT/s you get from PCIe 2.0 x16 is plenty for almost all games, it'll be a mechanical HDD that would limit asset streaming more than that.