I assume that you're doing this on the desktop, so the answer is yes you certainly can create a platform layer using libgdx, problem is this is going to be super messy because you'll have to pull in all the handmade source using JNI. (if you do this let me know as I want to see how it goes)
With that setup (ie you are only porting the platform layer), you can push that code to github, but you CANNOT push the actual game source or assets (ie gitignore the crap out of your repo to prevent this).
Now if you're going to port the actual game code itself, then I assume that you are writing everything from scratch... which is a bit of a gray area... and I'd assume Casey doesn't want a direct port of the game code floating around either. So if you go this route, you probably shouldn't publish it to github...
(disclosure, I'm taking care of the swift port of the platform layer, the native library interop is a bit of a pain in a managed language, be warned, thar be dragons...)