The alert should not appear. http://api.jquery.com/jQuery.ajax/ says:
In particular, calling .abort() on the object will halt the request before it completes.
And in the code:
// Allow custom headers/mimetypes and early abort
if ( s.beforeSend && ( s.beforeSend.call( callbackContext, jqXHR, s ) === false || state === 2 ) ) {
// Abort if not done already and return
return jqXHR.abort();
}
I believe this was in response to bug #8193 and possibly bug #10944.