Yes, the Editor class can support that set of scenario.
Once they've decided which layer to edit, you would set Editor.featureLayers to the layer in question, and set up the editing permissions appropriately using Editor.addEnabled, Editor.deleteEnabled and Editor.updateGeometryEnabled.
If you're using ArcGIS 10.1 the editing permission can be defined when publishing the service (instead of client-side with the Editor*Enabled properties).