Yes and No
Some vitamins and minerals such as potassium, B vitamins and C vitamins are destroyed by the heat and leached away into the cooking water , while other nutrients such as beta carotene [Carrots, Squash, Orange hue fruits and vegetables], lycopene [Tomatoes, guavas, watermelon, grapefruit, papaya, asparagus, red cabbage, mango] and phytochemicals become more accessible when cooked. Cooking breaks down the tough outer cells walls of these substances and makes them easier for the body to access.
Spinach is flaunted as a source of iron, however when eaten raw the oxalic acid it contains binds with the iron making it difficult for your body to utilize it. When spinach is cooked the iron is easily accessible to the body.
In Italy at The University of Parma a study was conducted which analyzed various modes of cooking vegetables to determine what effects these methods had on their phytochemical contents. Broccoli carrots and zucchini were used. They concluded that steaming and boiling vegetables preserved more antioxidants. They concluded that cooking in some cases increase antioxidant levels. Cooking softens the vegetable fibers, breaks down cell walls and increases the antioxidants acessability to the body.
1. Multiple studies have found that some vitamins, particularly many B vitamins and vitamin C are lost or diminished through cooking vegetables in water because they leach into cooking water.
Impact of different cooking methods on food quality: Retention of lipophilic vitamins in fresh and frozen vegetables