If the headstock is angled back, then just remove the string clamps and see if the strings are already lying flat across the surface of the nut. If they are lifted off slightly at the tuner side, then fitting a string bar is a good idea. If they are already flat all across the nut, then fitting a bar won't provide any extra benefit.

It certainly helps keep the tuning a bit more stable, means that clamping the strings doesn't affect the tuning allowing you to keep the fine tuners in the middle of their travel, and in some instances, has stopped a string buzzing sound coming from the nut. The clamps then simply are for holding the string in place, and don't have to force the string against the nut as well.