Gpu bottlenecking isn't really a thing. Monitor, cpu, and ram are though.
Gaming at 1080p? That combination is fine.
Streaming/recording? I'm thinking 720p 30fps is the limit with that setup.
3200g has few resources to spare - it's just 4 cores/4 threads, so you're mostly left with the streaming/recording to the gpu - assuming you get the RX 570 8GB model, as getting the 4GB one will further limit your options on graphics settings.
And all this still depends on the games. If the game is gpu heavy, forget about trying to stream it. Cpu bound games are probably doable.
Oh, almost forgot. You are also going to need that 2nd stick of ram sooner if you want to stream/record anyway. That lack of memory bandwidth is going to HURT.