Before getting into a real discussion of specific issues, you've missed one important detail- Why?
There are wireless solutions, where are Ethernet and fiber extenders, and there are long cables, each with different costs and drawbacks. Further, any solution besides directly running a pair of cables will result in some level of input and output latency.
With respect to HDMI audio, it works great on my laptops GTX675m (GF114), including DD/DTS 5.1 pass-through to a receiver, and I know that the HD6000-series works at least in stereo, and I'd expect them to work just as well as a pass-through device. Just don't expect them to send multi-channel audio that isn't pre-encoded, although they should technically be capable of this (shameless jab).
For HDMI audio in, I've never tried to do it, and have no idea how that would work from either an interface perspective nor a software perspective, so good luck with that one