It's definitely a bad idea.  That said, it looks like it's probably possible.  Something like (untested):
var appDir:File = File.applicationDirectory; // uses app: URI, can't be written to
var appPath:String = appDir.nativePath;
var writeableAppDir:File = new File(appPath);
var newFile:File = writeableAppDir.resolvePath("writeme.txt");
The nativePath and applicationDirectory documentation in the File class are full of warnings against this.  Follow them.
From the docs:
  Modifying content in the application
  directory is a bad practice, for
  security reasons. If you want to store
  application-specific data, consider
  using the application storage
  directory
  (File.applicationStorageDirectory). If
  you want any of the content in the
  application storage directory to have
  access to the application-priveleged
  functionality (AIR APIs), you can
  expose that functionality by using a
  sandbox bridge.