We have two instances of the widget running. The first is a Support widget on our Help Center, and that one is controlled in the Zendesk admin console. We've enabled contextual help and a contact form within it. It's great and totally works.
For the second instance, we added a separate version of the widget to another page and we're using it as a Feedback widget. We've been able to customize this widget a bit, but it's all in code. It would be awesome to have the same level of control and customization within the zendesk admin tool for all instances of the the widget.