Yes, in this case you can use the Linux side. To read analog data using the Arduino expansion board you’d have to configure the muxes to be able to get the correct data. Take a look at section 11.5 of Intel® Edison Boards — Intel® Edison Kit for Arduino* Hardware Guide
There is also some information on the MCU Quark and ADC here SparkFun Block for Intel® Edison - ADC Tutorial!!! if you are using the sparkfun block.