yep..it would work.. but we'd have to have al lour users accept the signature.. and there is no real reason we need SSL on TR.. they are still gonna see the GET requests in their proxy logs regardless of whether its a http or https resource they your requesting.
i'd not want to change the base that all the relative URLS pointed to unless we had a proper cert.
If your worried aobut your surfing being looked at, I suggest fidning a proxy to use