I think the answer is probably yes: a FileAppender owns an IDisposable Stream, and other appenders probably own IDisposable objects.
I would suggest having AppenderSkeleton implement IDisposable, rather than IAppender. The Dispose method would call OnClose. I also notice that AppenderSkeleton has a finalizer, which it shouldn't as it doesn't own any unmanaged resources. Do you see any problems with making the above changed?
