In Egypt I think it was more to do with the Nile floods - which no longer happen, because they dammed the river at Aswan. That said, it's fairly well-established I think that the line of desertification in Europe and North Africa was further south around the turn of the Common Era than it is today, though there seems to be contention as to precisely when and why it moved.
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.
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.