Dust can influence the climate. If there is enough dust in the air (either in a specific area or across the whole world) more sunlight is blocked and the temperature will tend to drop. Dust can also make it easier for clouds to form. This increases the amount of cooling and may bring more rain.
But we don't know exactly how much total dust is in the atmosphere and how much new dust is going up into the air today. So we don't know for sure what overall impact dust has had. All we know is that it does make climate forecasting that much more difficult.
Since solar radiation is limited by the amount of dust, we can say that the dust influences the climate, because it veils the warming effects caused by the increasing amounts of carbon dioxide in atmosphere.
Dust represent also a rich source of iron, so more dust means more plankton in oceans and more carbon in our atmosphere.