Would low doses of cocaine make society more productive, like coffee?
That was the thought in the late 1800s when black dock workers in New Orleans were given cocaine. The practice quickly extended to plantation owners as well. I think it only lasted for a couple of decades. By 1914 the New York Times featured articles claiming that negro rape of white women and other horrible crimes and uncivilized acts committed by negroes in the south was due to their use of cocaine. This of course led to many sheriff departments increasing the caliber of their handguns fro .32 to .38 to bring down the scary cocaine-crazed negroes.
Not sure if any real data exists from that period, but a number of peer-reviewed studies have shown that well-rested students who take cocaine before an exam perform, on average, better than their well-rested peers who do not take cocaine before the exam. Even more interesting, a 2013 study from Wake Forest showed that when rhesus monkeys were given cocaine for three weeks, then cut off completely, after a few days of painful withdrawal shock and delerium, they became 25% more efficient at simple tasks, on average, than rhesus monkeys who were never given cocaine.
Not sure about khat. I've only ever encountered it in National Geographic articles.