The short answer to this question is no. I don't know of any Application Server that behave this way. However, there are a few things that should be pointed out. Following is a simplistic explanation:
When your application server (ie. JBoss w/Tomcat) starts, it loads some classes in a class loader that will be shared by all applications. When it deploys your application, it will load those classes into its own class loader. When you undeploy your application, that class loader and all its classes will be garbage collected. So when the application is redeployed, all your classes are reloaded, and your singletons will be reinstantiated.
Your application will (in theory, atleast) behave the same after a redeploy, as after a JVM/Application Server restart.
Just a final tip: If you want to use the Singleton Pattern in your enterprise Java application, be sure you know the limitations of singleton objects in an application server environment. You can run into issues if you want to cluster your application, for example.