It is possible. To get around the lock on the JAR file, your application may need to spawn a background process that waits until the JVM has exited before deleting stuff.
However, this isn’t bomb-proof. Someone could install the application and then make the installed files and directories read-only so that your application can’t delete itself. The user (or their administrator) via the OS’es access control system has the final say on what files are created and deleted.