Even when you can use Debian, it is not suggested by Intel, yocto is.
You can upload sketches when the SD is not used since Galileo by default accepts sketches, it has (a minimal) yocto in firmware to do so.
This message was posted on behalf of Intel Corporation
As FGT mentioned, the supported image is Yocto.
You can use the Yocto SD image in order to upload Arduino sketches. It can be downloaded from the following link: https://downloadmirror.intel.com/24355/eng/sdcard.1.0.8.tar.bz2