How to use CKEditor for basic HTML formatting with webforms automatic emails?
I think the main goal is to receive HTML-formatted emails triggered by Webform module, right? This is how I achieved it:


Create and tune a new Text Format, specifically for emails (admin/config/content/formats)
Install Mime Mail module. It enables you to send HTML-formatted emails. Make it use the just-created text format in settings.
Install Mail System module. It provides you the UI for changing mail system globally or per module, if needed. Simply speaking, with this module you can easily configure HTML mail e.g. for Webform, but leave plain-text format for system emails.
You can use HTML tags in Webform > E-mails > Edit > E-mail template textarea. Mails from the website will be HTML-formatted.


Yes, it does not bind CKEditor to E-mail template textarea, but do you really need it? (If yes, I believe it is possible by creating a custom module that overrides the webform-email-edit-form form changing the element type from "textarea" to "text_format", see e.g. this topic).

Upd. I have just found a separate module for doing the latter thing: Webform Email Input Filter.