Use the top right Layers Control to dynamically add / remove Layer Groups from the map. Notice that child markers are actually added to / removed from the Marker Cluster Group!
This is the standard Leaflet Layers Control.
Note: it is normal that the computed clusters depend on the order of insertion. This is a result of Leaflet.markercluster algorithm.
Note: if your usage requires only compatibility of MCG with L.Control.Layers, you might be interested in this more simple plugin: Leaflet.FeatureGroup.SubGroup.