When I was looking for my last job, I explicitly queried about this:
"Will it be OK if I check my email only 3 times a day (at work)?"
In my previous job, too much work was done through email. Person wants me to do some work and return a plot. I send it to him. Within 5-30 minutes, he has a question about it. I have to respond soon. And it goes on and on - with each email interrupting whatever work I'm doing.
So I don't have "meetings through email" any more. They want to ask me stuff? Let's get in a room and at a fixed time and work through them.
"I keep my messenger app permanently off. Is that a problem?"
>but at the end you are interrupted every 5 minutes by people walking and talking/screaming/laughing about anything.
For me, this is a non-issue, and much preferred to emails and IM's. Especially IM. Also, phone calls are OK too. Why?
With IM, they start a conversation and then suddenly disappear, only to reappear 15 minutes later when I think the issue is closed and have started to work on something. No one does that in person (well, almost no one).
When they come to me in person or call me on the phone, they cannot just browse the Internet while talking. They are mindful of my time. And somehow, I feel they prepare their questions better, too.