Managed properly, yes. The soils of the Midwestern US were formed largely by herds of migratory bison for instance. The problem comes in when you don't defer g

Managed properly, yes. The soils of the Midwestern US were formed largely by herds of migratory bison for instance. The problem comes in when you don't defer grazing or give things a chance to regrow (see video in sib comment below). That absolutely can lead to desertification. As populations increase and nomadism becomes nonviable (so ground is not given a rest from grazing) it appears that's what happens.