actually you will have alerting when DB service is down because queries will be failing. But you have to know that such alerting may not work instantly after configuration of environment. You have to wait few days with traffic for creating baselines (failure rates are also baselining).
You can go to database instance in Dynatrace and setup static thresholds. They will be working instantly. They will also cover requests with small amount of traffic. This will give you problems notifications.