Currently the sidebar sections in the customizer will show/hide based on which sidebars are used on a given page (see #2). You can click around inside of the customizer to navigate to a page, and if that page template uses different sidebars, you'll see the sections in the customizer change while navigating.
It doesn't, however, hide widgets from the sidebar sections if they aren't currently rendered in the sidebar (e.g. via Widget Context or Jetpack's Widget Visibility). Perhaps the widget controls could be made opaque or minimized, for example:

See also: http://make.wordpress.org/core/2013/12/16/better-widgets/#comment-12125