Can ajaxSetup.success callback prevent ajax.complete callback from being called?

Question

In $.ajaxSetup.success I want a general piece of code to check something and then the $.ajax.complete callback should not be called. Is this possible? Preferably by doing something in the $.ajaxSetup.success callback and not in every $.ajax.complete callback.

event.stopImmediatePropagation might work, but I don't know how to access event from success.

$.ajaxSetup({
    success : function(jqXHR, textStatus, errorThrown) {
        alert('this will happen');
    }
});

$.ajax({
    url: '/echo/json/',
    type: 'POST',
    complete: function () {
        alert('this shouldn\'t happen');
    }
});

jsFiddle: http://jsfiddle.net/z4L4z3oo/1/