Badges don't have any relation to CW.
The original author of a post is the only one eligible to receive badges, just the same as how the original author is the only person who keeps the post in their user profile page. They were the original pen, no matter how many edits occurred.
It doesn't matter whether the post was CW first or not. I have a Nice Answer that is CW, in fact, and I originally posted it as CW.
CW posts actually make earning certain other badges easier, like Organizer. They're standard content for the site, so it's not as if there's any reason for a "catch" involved with them for badges. People can view/vote/favorite posts without any heed to their CW status, why would it matter to the badge system?