Most plant carbohydrates come from sugars, which are water soluble. Intuition tells me that if you boil the plant long enough, some of the sugars will leech into the water and you'll be able to drink it. As @SAJ14SAJ mentioned, green leafy things are usually pretty devoid of carbs, so you won't get much.
Also, as always, you'll get much more of the nutrients from a food by eating it, than juicing it or drinking the leftover liquids
The onion is one of the more "carby" vegetables that I know of, and according to this website:
about half of the carbs are from sugar