No, but there are still consequences.
"and catching up on work emails"
If everyone is doing this, there will be a expectation of you to do it. And if you don't - you will have to really shine somewhere else, to not get serious disadvantages.
Also I already had various big drama in my life for not being reachable (I still have a phone where I can put out the battery) - so yes, I know how to disconnect and I do. But there is an increasing pressure to be always reachable and when you don't live totally on your own - it is a real struggle to get away from it.