Yes, it takes about 10 minutes of cooking to destroy goitergens in plants.
If you buy a distiller remember to always add some minerals back to the water before drinking it. Distilled water, as with reverse osmosis, is very reactive and will not only remove toxins, but also vitamins and minerals from the body. By adding minerals back to the water the water will lose some of its solvency and become less reactive. This is why I prefer spring water to begin with. Of if I have to drink purified waters I add silica to the water to help saturate it.