For anyone else looking to further integrate New Relic, they offer an availability monitoring service. This way you can get alerts if Discourse ever goes down. (Ideally, that would be never!)
Discourse already has an OK status URL that works wonderfully for this purpose. If you go to your Discourse application in New Relic, then Settings → Availability Monitoring, New Relic asks for a URL to monitor. You can use /srv/status from your application, like https://meta.discourse.org/srv/status and hit “Save”.