Does it hurt to run a vehicle without a fan shroud?

Does it hurt the engine? Yes and no. It won't hurt to run the engine for a while. But running without a fan shroud seriously reduces the efficiency of the cooling system. Consider the shroud on a rad as a type of straw. Without it you won't suck much air through the rad. At slower speeds this will probably end up as an overheat situation. If the vehicle came with one, use it.