I've never had to install DirectX-anything for COH, since it uses OpenGL for graphics. Not on XP (IIRC) and definitely not on Win7. It does use DSound and DInput, but both of those are included in stock XP.
Running it in a VM, though, is something that has never worked. VMs typically don't have very good 3D support and most of that tends to be centered around Direct3D. Well, I did get it to run under VirtualBox for my quad box project, but it took hacking the game EXE to fix a bug that would cause it to crash when running with VirtualBox's GL passthrough driver. It wasn't exactly what I'd call pretty or very playable though.