Couple of small innaccuracies in the answer above:
2. A connection, be it RDP or other remote connection protocol needs to be kept open to the machine. Otherwise Windows will not render a desktop and you cannot run GUI tests. This is common to all GUI testing in Windows and not just TC. A popular method to do this is to run a tool like VNC server (or equivalent) on your testing machine. Configure the software to keep the connection open after you disconnect. This tricks the testing machine into thinking a monitor is attached.
Windows will always render to a framebuffer, no matter what. Whether that famebuffer is connected or nor to a screen is another matter completely. You do NOT need to keep a connection open all day long to the machine. The hypervisor (be it VMWare or Hyper-V or whatever else) provides a virtual monitor anyways. The problem with RDP is specific to RDP. When you establish a connection to a RDP server you are establishing a connection to a new or existing session. Locally your session is called the console session. The console session is normally only ever tied to the physical (or virtual) screen. When you connect remotely, a new session is created for you to work in. The problem is that when you log off, by default Terminal Services disconnects the remote session and connects back to the console session and then locks it. So, any other remote access service that runs as a service and does not lock the session on logoff will work fine, with or without you ever connecting to it.
If you are lucky enough to be running an enterprise version of VMware you can probably just connect through a console session to the machine using the VMware tools and no other software is required.
As noted, VMWare offers its own tokenized remote access protocol, and it is recommended you use it instead of RDP or anything else, as it works directly through the VMWare hardware abstraction and introduces no incompatibility whatsoever. However that is not only available with an enterprise license. Most people forget about the free ESXi! This is what I would recommend getting here, it's 100% free, the same solution as enteprise users, and the only real limitation of the free license is no remote management API (as in VMWare VCenter to administrate multiple servers). Each VM is still reachable with the remote console, and you can still use local APIs (the Guest API for example to control VM state from within the VM...).