<p>Can jQuery ajax made browser request a new location in redirect header send by server?</p>

Haven't tried jQuery, and a quick peek at the doc doesn't really tell me what a redirect response is handled as. But in Prototype JS any response code other than 2xx "Success" is a onFailure event, thus a redirect is a failure. You could probably parse the response (somehow) in the error block to see what code it is and get the address, wich you can set the document.location to... But it doesn't sound very safe, or practical.
It's more common to print an error of some kind.  Or, if the request requires a logged in user, to assume the session has timed out and redirect to the login page.