I'm using LINUX_IMAGE_FOR_SD_Intel_Galileo_v1.0.2.
which means you are on uclibc realms. I am not so sure about the yocto repo. I'd assume it's eglibc based. Then you wouldn't be able to run the packages even if install succeeds.
I downloaded the ipk file from http://downloads.yoctoproject.org/releases/yocto/yocto-1.3/ipk/i586/cups-dbg_1.4.6-r6_i586.ipk but I got an error after executing the command opkg install cups-dbg_1.4.6-r6_i586.ipk See attached image below. I have also tried building the Linux image using the Yocto Project but I never got to finish the build process due to multiple errors & I have no idea how to resolve the issue.
You probably are better off installing the non debug version (i.e. http://downloads.yoctoproject.org/releases/yocto/yocto-1.3/ipk/i586/cups_1.4.6-r6_i586.ipk) otherwise you'd have to install all the dbg chain. If the yoctoproject repo fits (not sure on that) you might also add it in /etc/opkg, e.g.
cat > /etc/opkg/yoctoproject-repo.opgk <<EOF
src yoctoproject-repo http://downloads.yoctoproject.org/releases/yocto/yocto-1.3/ipk/
EOF
after a "opkg update" you should be able to directly "opkg install" from this repo. "opkg list" would show you the list of available packages.