When our facility is using an ADC (load balancer), can I determine when the master is available and responding as expected?

You can view the status of the master node in Vocera Platform.

Using the VIP, log into Vocera Platform to review the cluster status panel displays with the details for each node. If the VIP is unresponsive then the issue may be either on the cluster itself or in the ADC configuration, and would require further investigation.