Does CoffeeCup offer a reader's comment section add-on? If not, I would like to recommend it. Seems like every site that posts an article, video, or picture has a post reader comment section at the bottom of the page.

If you are wanting the comments to be displayed on the web page itself, then no coffee cup does not have an application for that. You are better off trying to find your own PHP script for that. If you are wanting the comments to go to a specific person (via email), then you can use form builder for that.

Does Coffee Cup plan on offering an add on for comments to be displayed on a web page?

They do for their Stream content by enabling Disqus. If you want it for any page you can also use Disqus.