I believe most literature shows that MSCs gradually lose their multipotential capacity with culturing. Low passage have trilineage potential, they then lose chondrogenic potential first, then lose adipogenic potential and can only undergo osteogenic differentiation.
Our experience is that hMSCs from Lonza lose osteogenic and chondrogenic potential over the first 4 passages, and are generally very poor in p5 or later cells. Adipogenic differentiation remains quite robust in our hands out to p9. So relative to other lineages, YES, adipogenesis is preferred at late passages. However, how you define "late" passage may vary as a function of donor, tissue origin, and species.