Evan,
GCP launches itself after successful install - so yes, it is likely already there and you do not need to re-launch it. Normally it quietly runs in the background and the only indication is a little
"g" icon in the notification bar:

If you right-click on the icon, you'll see a menu with a few options and settings.
But the key point is that GCP is intentionally unobtrusive - its purpose is to make your computer a bona fide Globus endpoint, so that you could now access ist files from anywhere (e.g. try "Web: Transfer Files" item from the right-click menu).
Lev