QTP 11 supports running tests on on Minimized RDP(Remote Desktop) Session Windows

Just in case your’re looking for that feature - now it’s available :

If you want to run QuickTest in a minimized RDP (remote desktop protocol) session, and you are using an RDP 6.0 or later client, you can enable it by setting a registry value on the local computer:

1. Close all remote computer
2. If it does not exist, create the RemoteDesktop_SuppressWhenMinimized registry value (DWORD type) in one of the following registry paths on the remote computer:
   HKEY_CURRENT_USER\Software\Microsoft\Terminal Server Client
   or
   HKEY_LOCAL_MACHINE\Software\Microsoft\Terminal Server Client
3. Set data value To 2