What you wish probably won't happen. First, Even the switch at the bottom of the page would be different from a real logged out page. A technicality, I know, but still a difference that someone would surely object to.
Second, The "loggedin-ness" is pretty basic. You either are or are not. "Pretending" not to be logged in would permeate the code adding complexity and overhead for very little gain. Continue the way you are doing it, one browser for admin one for viewing the way the user sees it. Presumably you won't need to do the latter all that much once you get past the initial setup.