Does CyanogenMod include a kernel?
Looking at the repository for that device, I can see that the specified kernel is built from source using the source found here and the cyanogenmod_i9305_defconfig configuration file.

You can tell that the kernel is not the stock one by going to the terminal app (or from adb shell) and typing uname -a, which will tell you the build date of the kernel.  If it's the same as the creation date for the whole OS, then you know it's a custom-built kernel just for CM.

The CM11 branch also uses the cm11 branch of this kernel repo...