You can already do an inbox-zero-like workflow in slack.
In Prefereneces -> Sidebar set slack to only show "Unreads and starred conversations". This reduces the list of channels to these two things. (Edit: it might be a good idea to star all conversations that need followup, first).
Muted channels (which I make use of a lot) will still not trigger notifications, but now you'll know that, if it appears in the sidebar, there are unreads there.
I star any conversations that comes up and needs followups or actions. When I'm done with it, I unstar it and it goes away.
This has worked wonders for me and I highly suggest the same workflow to everyone.
Note that after the latest Slack update, it should be possible to make use of the groups feature and use them together with the workflow above. This way you can have multiple statuses like TODO, awaiting reply and delegated, like in the parent article, rather than a single set of starred conversations. So far I haven't felt the need for this personally.
Oh and one more thing. In Preferences -> messages and media set it to "Compact", it will declutter the UI a bit.
Hiding the list of conversations doesn't medan you have to keep away from them. You can still jump to windows and write to people using the search bars and commands! :-)
