app.config is supposed to be per application.
You can store connection string in separate text/xml file. Make sure this file is available during design time. Bindings will work, as long as file exists, and referenced appropriately.
To respond to changes at run time, You need to add a file watcher
] to the config file.
This is similar to how log4net watches config file.http://stackoverflow.com/a/372739/649524