http://tinycult.blogspot.com/2010/07/joining-machine-to-active-directory.html

  1. make sure that the machine you'd like to join to the domain is a member of the same Hamachi network as the domain controller
  2. it can see the DC.
  3. Ping std.hamachi.logmein.com to get the IP address of the Hamachi intermediation server
  4. On the machine that is joining the domain, set the Local Connection DNS setting to the Hamachi IP address of your domain controller.
  5. Now go into the Hamachi 2 client on the machine being joined to the domain.
  5.1 Go to Preferences, Settings, Advanced settings, Server connections, Server address 
  5.2 and hardcode the IP address of the Hamachi intermediation server there (std.hamachi.logmein.com).
  6. I was able to join the domain, I just had to manually input the DNS of the domain on the hamachi network connection
  

http://community.logmein.com/t5/Hamachi/Joining-a-Win-2008-domain-with-Active-Directory-using-Hamachi/td-p/50570

  Yes, that is indeed possible.  You would want to setup a Gateway network, which will allow your domain to handle DNS and DHCP requests.  
  This means that the Hamachi² net will pull IPs from your domain.
  
  

http://social.technet.microsoft.com/Forums/en-US/winservergen/thread/d98b2185-e64d-4243-ad9c-29cd512659b4

  ports for active diresctory
   
  if you want your client to be connected to domain it should resolve the dns query locally and also needs certain active directory ports
  to be opened and hamachi is the software provided by third party and will never open all the ports hence I dont think its possible. 
  To connect to your domain you will have to connect to direct VPN OF CORPORATE NETWROK OR  USE site to site vpn. 
  http://www.digitalforensics.be/blog/?p=94
  http://www.windowsnetworking.com/kbase/WindowsTips/WindowsServer2008/AdminTips/ActiveDirectory/WhatAllPortsAreRrequiredByDomainControllersAndClientComputers.html
  

http://kwjblogs.blogspot.com/2011/12/logmein-hamachi-commercial-as-global.html

  With the present versions of LogMeIn Hamachi 2, the software installs as a service and works without logging on.  That is possibly the most useful 
  feature as it made Active Directory Authentication over WAN a breeze.  Since the software is fast to deploy, all I had to do was install the client 
  on my Active Directory domain controllers, the IPv4 address assigned by LogMeIn Hamachi is sticky, so my DCs maintained the IPs after installation.  
  From then on, all I have to do is ensure that every system that is attached to LogMeIn Hamachi is given the DC's IP address as the DNS servers 
  (in the Hamachi Network Interface).   The result is fast, easy, and convenient Active Directory authentication over the internet.