I have been having this dispute for the longest time and I would like to know. Please, if possible, give some sort of scientific fact supporting your answer.
No, as others have said, it is a quick bread. This term refers to any bread that uses chemical leaveners (baking powder and/or baking soda) as opposed to yeast, and requires no kneading or rising time. The definition includes pancakes, waffles, scones, biscuits, coffeecakes, muffins and loaves. Obviously, quick breads are closest in texture/density and composition to muffins.
Many layer cakes use chemical leaveners, too, but the variations in the ratio of ingredients provides a much lighter, airier texture. So while the sweetness of Banana Nut Bread may remind you very much of cake, it is truly a bread!
Happy Baking! ~ Maria