Yes, as long as there is enough of an acidic ingredient to make a reaction (for 1/2 teaspoon baking soda, you need 1 cup of buttermilk or yogurt or 1 teaspoon lemon juice or vinegar). And remember that baking soda has 4 times the power of baking powder, so 1/4 teaspoon soda is equivalent to 1 teaspoon of baking powder.
Baking powder is mixed with the flour. When water is added to this flour to make dough, baking powder undergoes a chemical reaction during which carbon dioxide gas is produced. This carbon dioxide gas gets trapped into the dough and bubbles out which causes the cake to rise making it soft and spongy.