NASA seems to think otherwise though, expecting a 'dust minimum' to become a future norm.Interesting that they talk about the Sahara. Most of the Saharan dust that falls on the UK is quite large grit, much bigger than you need to nucleate raindrops.
Also worth noting that the Sahara probably isn't very old. There is evidence of grass and trees around 10 - 15000 years ago in what are now barren regions, and a suspicion that the present desert is to some extent man-made.
And whilst water vapor can supersaturate in very calm conditions, turbulence can initiate condensaton and crystallisation. There is plenty of turbulence in the upper atmosphere.