Depends on the image you have on the SD card whether it's supported or not.
If supported the Arduino IDE should upload the sketch to the /sketch folder and rename the binary to sketch.elf
The image I'm using is the one found here (https://software.intel.com/en-us/iot/downloads) which is the Linux image with IoTkit + LighttPD. So are you saying that if I power up my galileo, booting from the SD card and then upload a sketch via the micro USB, that it will automatically save the sketch to the SD card for use on future power ups?
yes - it will save one sketch. If you put another sketch there it obviously will overwrite the former one but will keep 1 old sketch as sketch.elf.old