Not unless you're a Twitch Partnered caster. 1080p needs too much bitrate. Use enough bitrate to run 1080p (3500-6000), and most who come to your stream will buffer like crazy and leave without saying anything about it.
The realistic maximum that non-partnered casters should stick to is 2000kbps to make sure their stream is most widely viewable, per usage metrics from Twitch. Partners can exceed this as they have transcodes (quality options) available.
Don't get lost chasing a number. It's very easy to blind yourself into the "MUST STREAM AT 1080!" or "MUST USE 60FPS!" mindset, and can be very hard to break out of if you let yourself forget that there's no point to streaming if no one can actually watch it.
On the up side, with that much CPU lying around, you should have pretty damn good quality for a 720@30, 2mbps stream, with the kind of x264 preset you'll be able to use. Most are kind of iffy, though watchable.