A relative URL without a scheme (http: or https:) is valid, per RFC 3986: “Uniform Resource Identifier (URI): Generic Syntax”, Section 4.2. If a client chokes on it, then it’s the client’s fault because they’re not complying with the URI syntax specified in the RFC.
Your example is valid and should work. I’ve used that relative URL method myself on heavily trafficked sites and have had zero complaints. Also, we test our sites in Firefox, Safari, IE6, IE7 and Opera. These browsers all understand that URL format.