Radar has a sufficient sensitivity to measure dust in the air. It may be possible to detect some dust storm over the source but the particles size has to be really large (at least larger than 100 micron). Particle size for transported dust is typically around several microns.
Lidar is definitely better than a Radar for dust measurement. The CALIPSO lidar is an effective remote sensing tool for dust profiling. For very dense dust, the CALIPSO lidar may not be able to completely penetrate the dust layer. There may also be some misclassification of very dense dust layers at relatively high altitudes and/or far north over the source region but the fraction should be small.