Oh well, it was fun to think about.
Bones tend to lighten (demineralize) with aging, and you often get calcium deposits in the joints. With rugged use you generally see muscle attachments that are more developed. Arthritis and some other medical conditions can make substantial changes, and those changes are pretty well studied.
But none of these changes are in the direction of Neanderthal. Take a look at the skulls, for example. Neanderthal is very much different. Aging does not lead in those directions at all. Part of the strength of Neanderthal was in the placement of muscle attachments; they were placed for more leverage and less speed that Homo sapiens. Aging would not change any of that.