Wikipedia says the Raspberry Pi supports "HDMI (rev 1.3 & 1.4)" and the HDMI 1.4 specification has Ethernet. Could you have a HDMI 1.4 to Ethernet adapter? and would the transfer rate be faster than USB 2.0?
2 Answers
Looking at the schematics of Model A and B Revision 2.1, page 2, as well as the schematics of Model B+ Revision 1.2, page 1, we find that the pin 14 at the HDMI connector is not connected. This pin is responsible for the HDMI-Ethernet-Channel (HEC) for HDMI 1.4 and reserved for HDMI 1.0-1.3.
So there's no HDMI ethernet connected on the Pi A/A+/B/B+ (and presumably neither on the Pi 2 and the Pi Zero).