Emacs 24 and TextExpander snippets not working
I would suggest that even though emacs is running as a Cocoa application, it is not necessarily using a standard Cocoa text input box / field, due to the complexities of a emacs enviroment. So emacs in this case is probably more similar to a X11 program wrapped into a Cocoa gui and does not know how to communicate with TextExpander.
As referenced from TextExpander Support, but anyways contact their support to get the definite answer.

Does TextExpander work with Java, X11, and/or Parallels?
Not at this time. Mac OS X's assistive devices key logging does not support these environments. TextExpander relies on assistive devices key logging to capture keystrokes and so does not work in these environments. We continue to explore ways we might support these environments in a future version of TextExpander.