You could rewrite your application so that it uses UserPrincipal.Current.EmailAddress
the first time, and perhaps whenever it is online, and then saves that information in the user's AppData folder or registry for reference when working offline. It would require running the application at least one online before working offline, but I don't see how else you could do it without having to ask the user or use a config file.
There is simply no way the System.DirectoryServices.AccountManagement
namespace will work offline. It's like asking how can a database driven application work without access to the database.