Keeping old site live while testing new site?
In short, yes you can, but this has a little to do with drupal. 
To clone a Drupal site is nothing more than copying the drupal root directory (codebase) and taking a database dump. It's quite easy then to transfer all these on any other environment and with some settings.php tweaking you will have an up and running clone of your site. The hard part is to migrate from D6 to D7, but you have already done this as far as I understand.

I would propose you to setup a staging environment by using a clone created from your local environment and start adding/editing content there. It dosen't really matter under which hostname that (staging) will be, it may well be the test.dept.university.edu  because you can make the production's url (dept.university.edu) to point back (redirect) to the staging machine when all things are in place and the time to go live has come.

This is a rough idea but I guess that the meaning is quite clear.

Let the mods to decide if this question should be close or not.