I'm assuming that you are using the Ethernet Shield, is that correct?
I've just tested it and I was able to connect the Edison to Ethernet using the Ethernet Shield. I ran the WebClient example without problems. However, there are two types of examples for Ethernet. One type of examples is named as "Ethernet" and the other type is named as "EthernetShield". Make sure you are selecting one example from the "EthernetShield" examples.
I am using the Intel® Edison and Arduino Breakout Kit
not with the ethernet shield by itself, I am able to access the web server, etc, ... without the need of an ethernet shield. Not needed for Galileo or Edison.
So I am not using SPI or use the pins 10,11,12,13 at all ???
For Ethernet/internet access I am using the WiFi builtin facilities of Edison. Works quite well so far.
I got confused. If you are using the embedded Edison's WiFi, what exactly is the question you have regarding the Ethernet.localIP() function on Edison? If you want to use the embedded Edison's WiFi you should use the WiFi library, but if you want to use the Ethernet library you should attach the Ethernet Shield because the Edison doesn't have an Ethernet port like Galileo has.
i use the std Arduino Ethernet library and it works quite well, that way my sketches work on the Galileos or Edison or UNO (with the Ethernet shield in this case of course) without or with very minor changes. I use the __X86__ and PLATFORM_NAME to guard those small differences.
THe TCP/IP stack is set by the operating system and the sketch just use the IP stack In the cases of Galileo and Edisons.
thanks for the help.