It's possible to deploy a Grails WAR file to a GGTS-managed server, but I've never done it. I'm sure it's easy to do, but I've never needed to. That makes a lot more sense in a framework that doesn't ship with an embedded (but complete) instance of Tomcat, and additionally the option to swap that out with a 1-line config change for a complete, embedded instance of Jetty: http://grails.org/plugin/jetty
When you run the app from within GGTS using the "Run As | Grails Command (run-app)" you're doing exactly the same thing as if you had run grails run-app from the commandline. All GGTS does to run the app, or tests, and even the generate- and create- scripts is call the same script you would, but in a separate VM so it's isolated, and it captures and displays stdout and stderr within the IDE. So it's very unlikely you're using tc Server (VMware is the company (or was, it's Pivotal now), vFabric is the platform, and tc Server is the beefed-up version of Tomcat that they sell licences and support for). If you want to be completely sure, go to the Spring dashboard and uninstall tc Server, unless you plan on deploying to it in the future and want to test that locally.
Another quick test is (assuming you don't have a custom 404 page) is to request a url for the correct host, port, and context, but for a nonexistent page or controller in your app. The 404 page should say Tomcat, but the tc Server page should say "tc Server", something similar to this: 
So if your app name is "foo", request
http://localhost:8080/foo/whereAreWeRunningFrom?
or something similar.
Also, if GGTS deployed to tc Server (or even Tomcat, but it's own managed Tomcat, not the embedded Tomcat inside Grails that it can't configure or access), it would do that by creating a WAR file and deploying it, and it would use the production environment. So reloading would be disabled. If you can change a controller, service, taglib, i18n file, GSP, etc. and the change takes effect, you're using the Grails-configured Tomcat. This uses an "exploded WAR" style of deployment, where it tells Tomcat that your project directory is an unzipped WAR file, and it configures the css and js dirs, the images dir, WEB-INF, etc. to point to your project folders unstead of a real unpacked WAR file.
You can run with SSL locally by using the -https flag, see http://grails.org/doc/latest/ref/Command%20Line/run-app.html - Grails will create a self-signed cert for you the first time, and you can continue using that, or use an approach like what's described here to replace it: http://grails.1312388.n4.nabble.com/Specifying-the-SSL-certificate-in-Grails-2-x-td4629128.html
