Is it possible to hack the "Correct spelling automatically" setting in OS X to emit a sound when correcting?
Not exclusively, but there is a tool that will mark spelling and other changes with a sound.

As described in this answer, it is possible to detect the type of text field change that autocorrect uses programmatically. A sound is issued whenever any of the text changes - but this results in a lot of false positive "sounds" when autocorrect did not happen. A proof of concept app was released August 2011, so I hope it is still fully functioning. Direct download link: http://cl.ly/9CIZ. The app works in the background, and has a few options, such as the sound to be played. The author of the tool states:


  Again, this doesn't work perfectly and has a couple of bugs but it
  should work 99% of the time!