Hey Evan,
Unfortunately this is a problem with WPF & WindowsFormsHost. See: WindowsFormsHost is not visible when AllowsTransparency=True. This can be fixed by using completely WPF code but we haven't had the time to do that.
In the WPF AutomaticUpdater we use the Windows Forms version of an animation control. This "native" control doesn't play nice with "AllowsTransparency=True".
If you want to fix it before we do, you can download the AutomaticUpdater source code. The "AnimationControl" will need to be converted to a WPF equivalent.