I want to have a field in a Drupal Webform where users can input some formatted HTML (tables, headers, etc.) Is there a way to do that?
Yes. The form element is called "Text format." This sounds like a format selector of some kind, but it's actually a text element. If you set it to "Basic HTML," for example, the CKEditor WYSYWIG loads. The image below is an example (the 'field' labeled Notes/URL(s)). If users wish to enter HTML directly, the code view button in the toolbar allows for that.
Here's what the initial page of the webform config looks like for this element...