On Windows you don't physically need a monitor hooked up, but in order to use D3D the video card needs to be set up as a display device with a compatible WDDM display driver. The same goes for CUDA, and I would assume OpenGL/OpenCL (I don't have experience with those so I can't tell you for sure). Nvidia has a special non-display driver called "Tesla Compute Cluster" that you can use for CUDA, which allows you to bypass WDDM. However only works with their (extremely) expensive Tesla line of video cards. There's a brief overview of the advantages here. On Linux the driver system is different, so it doesn't have the same issues.
Like Vilem Otte said, we use Optix for ray-tracing when computing our light maps. Our baking farm consists of a few PC's running Linux, each with several GTX 780's running in a non-display configuration. Ray-tracing is really natural to use for baking GI, since it makes it easy to sample your scene and it's trivial to parallelize.
If you don't want to deal with the mess of GPU's and drivers, you can consider ray-tracing on the CPU instead. Intel's Embree is very easy to use, and really fast. I don't think you could match the raw throughput of a monster GPU running Optix, but with a few beefy CPU cores you should get respectable performance.
Edited by MJP, 16 June 2014 - 12:26 AM.