Possibly. But I've noticed that during the process of stropping, my razors edge goes through different stages. Initially the hair will glide over the edge without being cut. Then more stropping. The edge will aggressively grab at the hair and pop the hair off. More stropping. The edge will gently grab at the hair and slice the hair up the middle. More stropping. The edge will ever so slightly grab the hair and the hair falls in two. At that point I'm usually done and can be assured of a good shave. The thumb pad test at this point usually reveals a very "sticky" edge.
But, often I will try the same with my wife's much finer hair (blondish red - finer than mine). If the edge will cut her fine hair I'm very satisfied. If not, again more stropping (usually this "more stropping" involves alternating between the canvas and the leather side of the strop). Usually I'll find one of her finest blondish, almost invisible hairs, and continue the process until that hair can be cut while hanging. Not a "popping off", but falling away. Once again, a good shave and "sticky" TPT.
Now it might sound as though I spend all day going through this procedure, but generally it takes no more than 10 minutes, if even that long, at most.
I contend that a hair's a hair and that if a razor is keen enough it will cut a hanging hair regardless of hair type. I'd love to be proved wrong (in other words I love a good challenge).
Scott
BTW - "good shave" = one pass, WTG, BBS shave.