That's basically what Quicksync will do. Shadowplay makes use of nvenc (which will consequently hammer your GPU, albeit with a relatively small hammer). You can also use nvenc in OBS, or software encoding (CPU). Using Quicksync will take the load from the encoding and put it on the Intel Graphics chip, leaving your CPU and GPU alone as if you weren't encoding at all.
One caveat: though it has gotten better since its inception, Quicksync (and nvenc for that matter) being hardware encoders, produce slightly lower quality videos (99% of people probably couldn't tell the difference, though) at higher bitrates (not great for streaming if you're super bandwidth limited) than what encoding by CPU can do. It's good enough for streaming, or locally capturing videos (at a stupid high bitrate, as lossless as lossy encoding can be) for editing later, but I still wouldn't do a DVDRip for my Plex server with it, mainly because I can do better with software encoding in both terms of quality (however insignificant, but worth mentioning) and resulting file size (actually worth mentioning, smaller files at the same quality are better!).
