In Halo 3 we witnessed/began the true fall of the Covenant. Hopefully in Halo 4 we can see some of the fruits of our labor in the form of a destabilized/broken Covenant.
There may be those that still try to follow the path i.e. zealous elites or such, the Kig-Yar are gonna go back to being space pirates, and the brutes will revert to being the undisciplined apes that they are. As for the grunts, they will probably continue to serve the ruling faction. It will definitely make for some interesting gameplay/scenes, that much is for sure.