I've been getting some spam in comments on my blog posts, so I did a bulk edit of all (115) posts, setting Comments to "do not allow." After which I (and presumably others) started received push notifications for each post, one at a time. Fortunately, I was able to go to the Plugins settings and disable the plugin before I received more than a few notifications (although the last few showed up as being "undefined").
It seems like bulk edits shouldn't trigger push notifications, especially when the only change is to the status of commenting.