We don't know yet...
Originally Posted by SoulReaver
It's currently unclear how long South American rain forests have been receiving fertilizer from the Sahara for and how they managed during the last green cycle, but forcing the Sahara to be green ahead of schedule may (among other far reaching consequences) seriously damage the rain forest.
That South American rain forests get a lot of their nutrients from the Sahara is a relatively new discovery. A lot more research needs to be done to figure out how this relationship has worked throughout history. It's possible, as you note, that there's a see-saw effect, so that when the Sahara changes back to a wetter/green climate, another part of the world dries up and sands from this new desert area make it to rain forests in South America. Sahara dust is not alone in feeding life in other parts of the world. Dust from other deserts feed phytoplankton in oceans, dust from Mojave Desert supplies nutrients to plants elsewhere in North America, etc.
Scientists can track dust storms today, but it's difficult to pinpoint sources of dust in prehistoric times, so while we know the South American rain forests get nutrients from the Sahara, we don't know where its nutrients came from millions or even thousands of years ago.