Dog urine and excrement are toxic to (and will kill) succulent green roof plants. Therefore, unless you have a green roof that is specifically developed for dog traffic, dogs should be kept off of the green roof.
If your green roof has been specifically developed for dog traffic, then it is likely vegetated with either a turf grass or a lily-turf, such as Liriope NoMo or Liriope spicata. Such roofs require a minimum of 6 inches of soil (the LiveRoof deep system), and should be cared for so as to preserve the plants material. Excrement should be picked up and the plants should be watered regularly, not just for hydration, but to flush the urine from the soil.