We've had a really fantastic experience with Slack. It's possible to do something kind of similar (but not the same) if everybody uses the same extremely complex set of email filters and labels... but in reality, email tends to work very, very, very, very differently from Slack.

Slack has very configurable notifications, so you can choose how much specific channels and conversations interrupt you, and you can choose how synchronous or asynchronous you want it to be.

Well-implemented chat is hugely valuable. It's hard to overstate how valuable it is.