No it does not. Because the plane of the Earth's orbit around the Sun, which from the Earth's surface is the zodiacal band in the sky, is tilted with respect to the equatorial plane of the Earth. As the Sun moves a degree per day along the ecliptic, for half the year it is above the equatorial plane of the Earth in the Northern hemisphere, and for the other six months it is below the equatorial plane of the Earth in the Southern Hemisphere. This causes, for northern observers, the sunrise/sunset points to move steadily northward between the spring equinox and the summer solstice at which point the Sun is at its highest noon elevation, and then move southward from the summer solstice to the autumnal equinox. At the Equinoxes, the ecliptic position of the Sun intersects the equatorial plane of the Earth in space.
Have a look at a basic astronomy text for more information.