If you add a bit of JavaScript with an on click handler to that HTML it will be possible for a user to manipulate the style to be hidden for the whole div. But of course it would be nice if that was just added to the documentation example - or even better as a standard feature.
While it is technically possible for a while to customize the welcome screen and/or the top bar it is not necessary straight forward and require access to the server where Windchill is installed.
I am supporting the idea that this Announcement bar is configurable using GUI when you are a business admin without accessing the server, playing with java etc....
and without restarting any servers (method, background etc....)