Maybe. One place I was at the CEO said everyone needed to be reachable on Slack within 15 minutes during work time. Nevertheless I would go offline for an hour or two at a time (which is as long as I can do deep work anyway) and it never seemed to be a problem. But directly disobeying the CEO always felt like something that was one unanswered Slack message away from disaster.
That is not true. It's embedded in the way we work and essentially not being on it is either not working, or not being part of the team. You have to use the tools of the job that your team is using.
(Not your job, Slack.)