I haven't looked in a while, but I don't think Drools even requires a webapp to run in. I think it's supposed to be usable in standalone java apps, too. So I doubt it's going to have a problem with Tomcat.
On the other hand, Drools comes embedded in the JBoss advanced server products (as does Tomcat), and the administrative support you get from such things might make it worth the extra heft of running full-on JBoss.
An IDE is no substitute for an Intelligent Developer.