No this is incorrect, I'm sorry. When explorer crashes, yes the GUI as you call it crashes, but that is because explorer.exe is the windows shell executable. When this crashes, windows automatically restarts it, and if not, it can be manually restarted. In either case, when explorer is restarted and the GUI is restored, tversity's tray icon is not restored as it should be.
When any application is started and has a tray icon, it must register itself as a tray icon with explorer's shell. This is typically done when it is executed the first time. However, if the application fails to re-register itself after explorer crashes, the tray icon will fail to reappear. Anytime explorer is restarted, it notifies all programs that there has been a taskbar refresh, at that time, all programs must re-register their tray icons.
This is an issue that can only be solved programatically by the developer, with a small change in the code.
This isn't 1998, all modern programs should be listening for explorer updates, and thus recover the tray. It's unfortunate that tversity does not.