no, you don't need EDKII & Grub for a new kernel / module.
I guess the easiest for you would be to either chroot into a Galileo image (e.g. mount the SD card from your Galileo on a host and chroot into there) - or to generate a virtual machine image and work on Galileo in a virtual machine. The image should obviously have devtools and kernel sources installed.
Why going via 1.01? I'd assume you can work directly on 1.0.2