Azure SQL and Storage accounts can now be connected to an Azure VNet using Virtual Network Service Endpoints.
Are there plans to update the JIRA Data Center on Azure templates to leverage this feature?
This is something that I believe Atlassian announced a greater support for at Summit a few months ago. As such I would recommend checking out the page https://www.atlassian.com/enterprise/data-center/azure .
That page does have some links to some additional guides for setting up data center on Azure such as Getting started with JIRA Data Center on Azure.
I can see that Azure SQL looks to be gaining support here, but I have not found specific documents in regards to the using the Azure VNet you mentioned. But I think that the diagram on that page is referring to using the private virtual network for the Jira nodes on the back end, while the NAT would sit in the public network.
Does this help?