No, as far as resource management goes each webapp is totally isolated from every other webapp. In the
Tomcat server, there is exactly one and only one WAR per webapp (and
vice versa). In full-stack J(2)EE servers, a webapp may contain multiple WARs, but normally each WAR has its own unique classpath, so they can't share objects directly.
Webapps are supposed to be self-contained and not be looking outside themselves for code resources.
However, if you provide a web service interface (
SOAP, REST or whatever) to the services of a class in a WAR, other WARs (webapps) can invoke those functionalities by making HTTP service requests.
The secret of how to be miserable is to constantly expect things are going to happen the way that they are "supposed" to happen.
You can have faith, which carries the understanding that you may be disappointed. Then there's being a willfully-blind idiot, which virtually guarantees it.