I had that combo (no rx 480 anymore), was working buttery smooth, but keep in mind that at Full HD the CPU becomes the bottleneck, it´s still not noticeable at all compared to a higher clocked CPU from the blue team (Skylake, Kabylake and since yesterday Kabylake-X), the differences are marginal and if you don´t have a high refresh monitor you can´t notice that anyways. I kept my 1600x because of its versatility and the rx 480 is a solid bang for your buck as well, go ahead and have fun