It can, using either basic auth or by scripting submission of login forms.
Probably obvious, but you should avoid doing it from one of the public instances. Building your own private instance is as easy as spinning up a prepared EC2 image, or if you have a couple of hours to fiddle about you can do it from scratch on any Windows machine. Details here:
Can WebPageTest (I've never heard of this tool) reach pages that require authentication?
http://www.webpagetest.org/