Absolutely (and not just civil ATC training - military as well). A large part of modern ATC training is simulator training. This is true for all types of ATC - area control, approach and aerodrome (tower).
For area and approach, the simulator is fairly simple, since the essential bit is a radar screen and a screen with flight information. For tower, there is the visual aspect as well, which makes tower simulators quite large and complex. Some tower sims are relatively simple - 4 big TV-screens with a 3D model of the airport, and a couple of computer screens with radar and other equipment. There are also full size, 360 degree sims, where the "windows" are created by an array of projectors or large screens. After working traffic in one of those for a few minutes, you start to forget that you're not in a real tower.
During simulator training, students can run scenarios in the simulator that are either based on generic airports or real airports. The traffic levels and situations can be tailored to match the expected learning curve of ATC students. This makes simulator training a great tool for both initial and recurrent training of air traffic controllers. Much like pilots, after getting our license, we have to go back to the sim once a year to practise unusual situations, emergencies and so on.
For every controller position in the simulator, there are 2-3 connected "blip driver" positions, from where the aircraft movements are controlled. The controller in the simulator will talk to the blip drivers via "radio", and the blip drivers will respond as pilots and provide the necessary input to make the planes move around accordingly.