Not really, there's several problems there. Completely ignore people and they'll just start complaining about that, and it does happen that people just need you to make it more obvious that there's a problem. It also means that it's less clear if you're not responding to things because you're just busy, if you're not responding to things because there are things that need to be corrected or if something else is going on.
It's just a generally bad way of correcting people's behavior.