We have an Active Directory domain sitting on a networked Azure VM and have a separate Azure WebApp/Website that is running Orchard CMS on the same virtual network.
Yes, you can connect your web app to Azure Active Directory.
The simplest option is Azure Easy Authentication
http://azure.microsoft.com/en-us/documentation/videos/azure-websites-easy-authentication-and-authorization-with-chris-gillum/.
That's a one click way to authenticate your site.