I have -up2now- not seen 1 device, where the combination of HW/SW was capable of offering ethernet to the Device OS.
AFAIK, no (mainstream) PC/Embedded/Mobile graphics chip/firmware/driver combination supports this. Please do indicate a counter-example, if you know of one.
I consider that unlikely to change too, since Ethernet is limited to 100Mbit over HDMI. Gigabit (Wifi) ate that lunch.
Outside of "Device-Collections" from e.g. B&O, that might use that comm-channel to have a "guaranteed communication backend" available, I see no real (commercially) interesting reason for implement it.
Having said that, I'd be very happy, if GFX-card/TV vendors started implementing the optional parts of the HDMI spec, like CEC,ARC, and Ethernet. I'd find use for it.
We're not there yet, but we're on our way. My Philips Ambilight TV pops up a warning every few weeks to remind me that I should connect the TV to the network to benefit from all the smart apps it has bundled. Immensely frustrating.