Q. Can DNS on Nano Server be AD integrated?

A. No. While DNS is supported on Nano server with the 2016 RTM of Nano the DNS must use files and cannot be AD integrated. Note DNS can be installed at image creation time or post install using:

Install-PackageProvider NanoServerPackage
Import-PackageProvider NanoServerPackage
Find-NanoServerPackage
Install-NanoServerPackage –Name Microsoft-NanoServer-DNS-Package
Enable-WindowsOptionalFeature –Online –FeatureName DNS-Server-Full-Role

In the example commands I first install the NanoServerPackage manager then use it to view available packages online (remember with Nano if the image was not built with the component it is not present on the file system (sxs) so has to be actually downloaded to be installed) and then download DNS and enable it.