If you will choose to leave the mapping and model files on the file system and not re-add them as embedded resource,
so after applying this change, the connection strng for the EDMX is changed, and the "metadata" property for the connection string is change to refere the specific files from the file system (the ssdl/csdl/msl) instead of their old location from the assembly resource, so you need to update your connection string at the executing assembly app.config (or the web.config).
Another thing you have to do, is to include the model.ssdl/csdl/msl into the project and set their "Copy to output folder" property from "Do not copy" into "Copy if newer" or "copy always" so when you build your project, any project that reference your EDMX dll will have them in his bin and the connection string metadata will be able to find them.