Ben, besides Tomcat you also need the database to be running to have Activiti working properly.
If you're using the standard demo.setup, then it is not going to be so easy (because you would need to call a .bat file when the service is started, which can be tricky if the bat file doesnt return). If you're using a 'real' database (eg MySQL), then it becomes more easy, since that can be configured to start when the system boots.