Not really, no. For one thing, if humans were in the Sahara then to get out of Africa they would have to cross the Nile...not an easy task for people who lack the concept of boats or at least rafts. Second, much of human development is supposed to have come from the Tanzania region which would at least get them on the right side of the Nile but is a bit too far south to be considered the "Sahara." Third, even today as the Sahara creeps south, people do not move. They sit there and watch their farmland turn to sand unless a war breaks out and then they become refugees.
The whole question of how and why people migrate is another fascinating topic, though.
The whole question of how and why people migrate is another fascinating topic, though.