In theory, yes. What game are you streaming? Settings can vary quite a bit depending if it a strategy game lie starcraft or FPS like CS.
From what I've talk to others about you rarely need to push more then 4k with a 1080p stream regardless of how big your connection is since you will only decrease the amount of people who can watch it.
Why? If you set the bitrate/buffer to, let's say 4k/4k, your viewers need to have a 10Mbit connection at least to be able to watch it smoothly. The less bit/rate buffer you have, the less strain you put on the viewers connection.
Since a low bitrate will show a lot of pixels on screen because it's compressed you can even this out if you have a monster machine by going down to "fast" on x264 preset but with your machine I would not go there.
The FPS part is a lot more dependant on your CPU so exactly what i7 is it? I have an i7-2600k clocked to 4Ghz and I'm struggling to push 59fps with 1080p.