A tool such as Tourbus might work. It's a Ruby app meant to stress test Web sites. It uses Webrat and (I think) Mechanize underneath, and does not open any browsers.
If the site in question has scripting you're out of luck, but otherwise it should be quite useful.
In fact, I found yourself using both Tourbus and Selenium on a project, and decided I didn't want to have duplicate tests, so I wrote some helper code to allow Tourbus to execute my Selenium scripts. So far, so good. I can record the actions in the Selenium 'IDE' plugin, and use them in Tourbus.
If the site in question has scripting you're out of luck, but otherwise it should be quite useful.
In fact, I found yourself using both Tourbus and Selenium on a project, and decided I didn't want to have duplicate tests, so I wrote some helper code to allow Tourbus to execute my Selenium scripts. So far, so good. I can record the actions in the Selenium 'IDE' plugin, and use them in Tourbus.
http://github.com/dbrady/tourbus