Could i ask why you would want to do this?
Your header is your main identifying marker for the site. Having a blank page or a blank header area wouldn't make much sense, because it doesn't inform the guest why it is blank. turning off all the links on the page when it is being viewed by a guest i can understand. Personally i would like my sites name being there, heck id like my sites name being on top of everyone's page for that matter. the more the better. :)
I would suggest that you find the CSS code controlling the header. In your Templates/Base/Css/general.css I think there is a section labled Logo or something like that. Change the display to hidden or reduce the min allotted pixel size to 1. something along those lines so that you would not have to change the loading process of every page.