While it would be feasible to do this on a headless server with a beefy processor and minimal graphical power, you're almost certainly going to get better results if a decent enough GPU is used on the host.
Ideally, the hosting machine would need to be powerful enough to play the game and to encode the stream simultaneously.
Does the hosting machine need powerful graphics or would a headless Xeon PC server work well? I ask as I am looking at getting one anyway to host opensim and that only being a database doesn't require much in the way of a GPU the graphics being handled by the client viewer.