The juice is a kind of fasting. I don't think it's beneficial to do Water Fasts because you need the nutrients, and the anti-inflammatory properties of the juice is very important for healing. You actualy don't really need extra vitamins with the green juice as it is packed with nutrients. If you can I would get as much sun as possible for vitamin D but taking some vitamins shouldn't be a problem. I try to get all my vitamins and minerals from food with the exception of some extra b12, Iodine and selenium and the vitamin D when I don't get enough sun, which is most of the time.
Actually I think it's best to use pulpy juce which is what the masticating juicers produce as long as you don't strain it. Smoothies would work too but that needs a powerful blender and it's hard to get fibrous greens really smooth so I prefer the juice. You could add juiced greens to a smoothie though.