Eek -- this seems to be a step in the wrong direction from work/life balance.
Extremely important issues don't come up that frequently. So I'll be the judge of whether I need to deal with it now or it can wait and be on the docket first thing in the morning
The reality is for most of us, when we're tagged on some issue, our reaction is to at least check it out and assess the priority, etc.
Stuff like this isn't ruining work life balance. They employee is by engaging and allowing the behavior outside of work
What scenario do you anticipate people using this app? In the middle of meetings with other people? While driving? While sitting in the cafeteria on their lunch break?
One of the most important next things we can build are more controls in when/how you can be reached (e.g. setting working hours).