Knowing that messages are removed speedily from Azure Storage Queues is important to know. It is also a completely different problem then knowing when messages are being deadlettered due to errors in processing.
A good way to know when messages are NOT being depleted or are not being depleted fast enough from a queue is by letting CloudMonix alert on the age of the next-to-be-depleted message. This is easy accomplished by tracking metric of type AzureServiceBusOldestMessageAgeInMinutes and comparing it to some number of minutes under which queue is expected to be depleted. Depending on specific use cases, it maybe a good idea to have CloudMonix alert only after a sustained amount of time when age of the next-to-be-depleted message is too old.