Quick answer - kind of
Long answer - read below
Windows Server AD
Instead, the programmatic directory service interface for Azure AD is the REST-based Graph API .
Instead of developing a separate identity store and authentication process for each discrete cloud application, Windows Azure AD provides a single identity service that can be leveraged by all of your cloud applications.
Azure AD can also be integrated with an on-premises Windows Server Active Directory infrastructure via Directory Synchronization and Active Directory Federation Services (ADFS) to provide single sign-on to Enterprise users for both on-premise applications as well as applications developed for the cloud.
My colleague Keith explains here:
The built in Azure DNS doesn?t have all the features needed by Active Directory, such as Dynamic DNS
Here are some links that might help
Azure VMs using dynamic IP that are constant for the lifetime of the VM
To overcome this issue, you will need to provision a Windows Azure Virtual Network prior to attempting to provision the first domain controller VM
For disk access speed, Azure uses Read-write host caching. But there is a slight chance of data loss.
To overcome this, attach a second empty disk to our VM that we format and use for the NTDS DIT and SYSVOL folder locations
For step by step instructions, see this post: