You mentioned your hardware not being up to the task, what do you use?
Btw, I'm planning on streaming Console only so my graphics card might not be such a big issue or am I wrong?
My desktop has an i5 2500K, 16 GB DDR3, and a GTX 680.
The graphics card and CPU end up being factors, because the computer you're rendering the video on still needs to perform graphical tasks. You'll be eating up a fair amount of resources with the streaming & rendering, but it is significantly less than if you were also playing a game at the same time (that's why single-PC twitch streams tend to have a harder time hitting 720p60 or 1080p60). So yes, though you're doing console games, the streaming computer is still a factor.