Can uneven heating of air in earth's atmosphere cause convection?

Actually, it's the uneven heating of the Earth's SURFACE that is the cause of most convection. Sunlight hits the ground. Depending on what sort of surface it is, more or less of the energy is absorbed, or the sunlight reflected. Snow and ice reflect more; light hitting at low angles of incidence are reflected. Sunlight hitting paved roads or plowed fields are mostly absorbed. The hot dirt and roads heats the air above them, causing the air to expand and rise; the cooler air above is more dense, and sinks.