Well, set it up the way it is supposed to be and see if you can get to the pages. Test it the same way you would a single, solid website. However, Tomcat is a JSP server. Usually it is the other way around:
SomeWebServer (Apache httd or IIS) --> Tomcat
Any redirects from Tomcat would be in the form of directly included URLs.
What's so evil about running Tomcat behind IIS? :-p. I've used it before when we had an existing IIS website and needed to run a JSP webapp. I've also used Tomcat as a standalone http server many times including my current home server and our division intranet site. However, it doesn't support virtual hosts and all the other nice things like Apache and others do, hence my reference to usually being behind a more capable web server.