I have a ServletContextListener which performs some database management functions when my Java EE application starts. This runs in my application before JPA and other pieces
If your ServletContextListener throws an exception, the webapp won't load correctly and the application server may block all subsequent request (and respond with a 500 error).
It isn't exactly preventing the application to start, nor stopping the application, but it prevents any further usage of the app and could be useful in your case.
After proper verification in the spec, this behaviour isn't mandatory in the specification. The server may (not must) return 500 errors. This solution has to be used carefully, therefore.
See this Answer for a quote from the Servlet spec.