Yes, it sure can. There's two ways sites handle logging in: via authentication (where your browser asks for a username and password), or via cookies (where you use a login form on the page). Simon can handle both.

If the site uses authentication, you simply enter the correct username and password in the Security section of the Edit Test window.

If the site uses a form and cookies, you can visit the page in the Preview window and log in while the Edit Test window is open, and it will record your cookies and use that to log in later.