There are streaming options that don't add much CPU processing. For example, NVidia Shadowplay. AMD's solution probably works okay too.
You also don't give any other info about your system.
As said above, streaming (uploading) can be problematic. You can run "speed test" and see what bit rate you can upload. I get only 0.7Mbps which means a fairly low quality video.
*The minimum NVidia Shadowplay shows in the settings is 10Mbps, though I can record down to 360p, LOW quality so I assume it would end up a lot lower. I'm going to test that now..