Wouldn't messages syncing to all devices, which might be a concern if you wanted the detection to be covert and only get alerts on a devices you can trust to be on your person? i.e. the 'unrecognized person' won't see a new email coming in to tell them they've been spotted and prompt then to cover their tracks.

To this point, the app holds its own desktop notification until it recognizes your face again, and only then tells you who came by. Remote alerts are instant.