Async is for the area between "Slack" and "Documentation" -- it covers things like project statuses, requests for comment, new feature discussions, company announcements, Friday updates and lots more. You can think of it like a cross between a blog and Twitter feed. We're starting to add more Reddit-like features for customizing the experience and sub-groups but that is pretty early still.
I don't think Async solves the problem you mention -- that is more of a cultural thing. We expect folks to message each-other frequently (preferably in a public room with an @ mention) but set the expectation that you don't need to respond immediately. The public aspect is important as you will often get "drive-by help" from someone else on the team!