Hopefully a more experienced Godot dev will jump in and correct me if I'm wrong here..
Godot uses reference counting, but additionally supports a function which you can call on an object which will cause it to become 'unmanaged' by the reference counter, allowing you to free its memory on your own terms (or leak the memory, if you're not careful).
Godot 3.0 added support for Mono, but I'm not sure how that works. I'm guessing that game objects in Godot are still reference counted, but now you also have memory allocated by the Mono runtime which will be garbage collected.