Not under the active apps but as a background process and it is unlikely to get noticed near the bottom of the list because the CPU consumption stays low at first. Eventually it will start draining resources and spike up as if the game is up and running, when it is not
Sometimes the game will launch without an icon on the taskbar and the whole badge will be just blank space. Often after closing this instance of the game the problem I described in the first paragraph tends to occur. Additionally the scroll wheel over the character list might feel unresponsive until I alt-tab out of the game window a couple of times.