Unfortunately the answer is "it depends" depending on your game and settings the 1600 can manage it, but would be easier with a 1700. You can also offload a lot of the encoding work onto your GPU in which case the 1600 would be perfect, but you tend to get lower visual fidelity.
That being said I'm not yet sold on the idea of 1080p60 in a single system. 2 systems, yeah sure, why not. But with one it feels like more effort setting it up than its worth, going for either 720p60 or 1080p30 depending on what sort of game you want to stream you can get very good results for half the resources you need with 1080p60, my personal opinion, unless I really look closely I don't notice the difference between the three, and I'm much happier watching a stable 720p30 stream and a 1080p60 one that keeps dropping frames.