It will not work like that, the call $('a').click();
is a short cut for $('a').trigger('click');
which tries to simulate a click action on the anchor element.
But the simulation is not absolute, though it will fire the registered event handler it will not completely simulate a use click trigger the default action.
As per the jquery doc for trigger
Description: Execute all handlers and behaviors attached to the
matched elements for the given event type.
and
Although .trigger() simulates an event activation, complete with a
synthesized event object, it does not perfectly replicate a
naturally-occurring event.
So I don't think it is possible to completely simulate a user action and trigger a redirection using this method