I don't know about the streaming, but I would probably go for a R9 285, it's not that much of a price jump, or a GTX770. And, you defenitely want to get a better cooler than the stock Intel one if you think about seriously overclocking that CPU.
Streaming will cost you some performance and therefore a quad or six-core AMD might be a better choice. But you can also try it out and eventually swap the Pentium for an i5 or something. Should be decent for now.
With typical H.264 encoding by the CPU, two cores is nowhere near enough. However, I'd suggest trying out AMD's GameDVR, which can be used with Raptr.
http://raptr.com/
I use this to record videos(can stream as well, but my internet is shit), and have little to no performance hit. It's essentially AMD's version of nvidia's shadowplay. Setup is a bit weird in the beginning, but as long as recording/streaming options are setup and enabled, as well as the in game overlay, it should work just fine.