WordPress does not need Tomcat.
All WordPress needs is…
To run WordPress your host just needs a couple of things:
- PHP version 5.2.4 or greater
- MySQL version 5.0 or greater
Plus adequate RAM– 32MB for a single site, 64MB for Multisite. Many hosts these days provide much, much more than that by default.
I don’t know if there are plugins (or themes) that do, but certainly you can check the Docs for your plugins and find out if any of those need it.