According to the schematic (https://communities.intel.com/servlet/JiveServlet/downloadBody/23309-102-1-27413/edison_arduino_hvm_8_26.pdf) only I2C6 is brought out to the arduino headers both as A4/A5 (on the 'analog' headers) and SDA/SCL (on the 'digital' headers). I tested my board with my multimeter, and indeed A4 and SDA(on the 'digital' headers) have continuity and A5 and SCL have continuity.
The reason I2C1 is not brought out on the Arduino Edison board headers is because I2C1 is used to provide all of the pin-muxing capabilities.
I do agree that having the ability to target both I2C1 and I2C6 on the mini-breakout from within the Arduino IDE would be a nice thing to have for people who want to stick with 'Wiring/Arduino' as the programming interface.