If you have your site in offline mode and log in at the frontend, the site will display as normal, however others trying to access the site ( in this case the w3 - validator?! ) will still get a 503 Service Temporarily Unavailable -response. It is not not possible to validate the website while it is in offline mode (but it is easily forgotten that you logged into the page).
To validate the site during development you can set the site in online mode, and protect it with .htaccess-authentication ( http://www.htaccesstools.com/htaccess-authentication/ ), this will pop up a login-box in the w3 validator.