Company of Heroes runs just fine as is under Windows 7 (Vista as well). DX10 & 11 both fully support DX9 calls.
Both Windows 7 and Vista will require you to install DX9 if the game need DX9. It does not come installed by default with Windows 7 but both DX9 and DX11 will coexist just fine it just needs to be installed. How ever most games will install the DX runtime if it is needed as part of the install.