That's the whole point of my comment. Email is less efficient so it will discourage unnecessary communication. Only the important information is divulged and the useless chatter forgotten.
I'm serious, but of course your manager needs to support you in your decision. For me Slack represents a 20-30% productivity hit, and it should be Slack that justifies taking up my time rather than vice versa.
If someone needs to talk to me, they can email or approach my desk. I know this approach wouldn't be practical for remote teams. But perhaps some of the async communication options like Twist would work well?