In a word, Yes. Tomcat is an "Application Server" for certain types of applications, including a large percentage of the applications being developed today. The answer depends, of course, on your definition of “Application Server”. It also depends on whether you think Tomcat is limited to the Apache Tomcat Project, or whether Tomcat also includes all the add-ons and plug-ins that have been made available through open source or commercially.
In any case, I assert that Tomcat is indeed an Application Server, all by itself. Tomcat becomes a much richer Application Server as you modularly (the only sane approach, IMHO) add functionality as required by your specific application.
So, what’s an “Application Server”?
I frequently hear the questions “What’s an application server?, “Is (or isn’t) XYZ an application server?”, and “Do I really need an application server?”. These questions also show up in various internet FAQ’s, blogs, etc. Some of the resulting discussions are almost hilarious, with firmly held beliefs sometimes swamping rational thought and one recent discussion at a major client bordered on open warfare. I too have some opinions, though perhaps not as vehemently held, based on years building applications across many architectures and technologies.