It\'d be convenient if an application I\'m writing stored some files to external storage permanently (so they persist after the application has been exited[destroyed]), but
Yes, this is possible. Simply write your files to the external files directory:
File dir = getExternalFilesDir(null);
This will create a folder at /Android/data/your.package/. Note that this is not External as in sdcard, but it is publicly accessible. If a user uninstalls your app, this directory will also be removed, along with all of its contents.