Is there a plugin for FireFox that will allow me to view a website as if I was looking at it in IE 6?
Unfortunately not, however there are a great number of on-line services that you can use for testing, or you could also install a stand-alone version of IE6 for testing on your own PC.
On-line renderers:
http://netrenderer.com/
http://browsershots.org/
http://www.browsercam.com/
Stand-alone versions of Internet Explorer:
http://tredosoft.com/Multiple_IE
The benefit of an on-line renderer is that if it's just a display issue you wish to see in action, it requires the least amount of effort and is generally quite quick to test out.
The benefit of the stand-alone solution is that you'll be able to actually click on things and practically use the site as you would in any other browser which might uncover specific problems that only occur due to a particular user interaction (clicking on a link or button that's being manipulated via JavaScript, for instance).