Indeed, I always thought the theoretical benefit of dying gasp was for example to stop prevent the DLM from taking emergency punitive action when a large number of 'lost sync' events were seen in a short time, used to be ten in an hour, earned an immediate and semi-permanent 6dB on margin. Was designed to quickly stabilise a duff line and make it usable.
The problem with above is, of course, if you're spending an afternoon experimenting with wiring changes its all too easy to hit the threshold... been there, got t-shirt, etc. If however the router is able to send a dying gasp before the connection goes down then the DSLAM ought be be able to tell DLM not to count it as a 'fault'. Unfortunately I seem to remember convincing myself that the DSLAM actually took no notice, so don't pin your hopes on it.
Above is based on 'old' 8 Mbps ADSL, I know the rest of the world has moved on but similar principles may persist.