A quick look over the rfc's for the http indicate there is no referrer controls. So the answer is, maybe. Since there appears to be no defined referrer handling, it is up to the browsers and servers to determine what they want to do with it, and will provide no guarantee as to what if any data it will have. Referrer is already an unreliable method of tracking, so you'll need to use an alternative means such as a querystring.
header('HTTP/1.1 420 Enhance Your Calm');