The movement of deserts in North Africa was then caused by long-term climatic cycles, nothing that humans could change back then. If you want to look at some example of desertification in history caused by agriculture, Mesopotamia would be way better example. However, Romans managed to degrade Mediterranean ecosystems - but not through agriculture, but through industry. Preindustrial Premodern industry requires fuel just the same way the modern one needs it, but the only source it usually have is wood. And it needs lots and lots of wood for metalworking and glassmaking, as a building material for both houses and ships and as a simple fuel source for cooking and heating. Romans took whatever wood was available, turned some of it into ships and then turned the rest into charcoal. But to be fair, many Mediterranean cultures managed to deforest themselves pretty successfully without any Roman help (I am looking at you, Greece). It was similar deforestation that Western Europe gone through that resulted in peak wood in the 18th century, but the wetter climate is more resilient and the West and Central Europe is suffering now from biodiversity loss from reforestation. It is the same need for charcoal that is is making desertification in the Horn of Africa even more serve now. Really, one of the most beneficial discoveries for environment are fossil fuels.