If my GPU can process basic Compiz effects as seen in GNOME Classic, will they work in Unity 2D?
Probably. The goal of Unity 2d is to provide a unity-like desktop to those whose "hardware platforms cannot currently support Unity's OpenGL requirements". Check their wiki page for more info: https://wiki.ubuntu.com/Unity2D.
As I found out (after reactivating Compiz,
compiz --replace), those effects are indeed functional within Unity 2D.