People say ume is hard to root, and it is. But I've been able to root a few each year. Problem is those that root would gradually die by late winter/early spring. Could be a fungus problem. Anyways being able to root some ume would make me optimistic rooting cuttings from peach or nectarine.
On a related note, this discussion made me do some online reading as to why people prefer grafted peach. Those reasons may not be so relevant in bonsai if the stock is meant to be container grown all it's life; the reasons may be more relevant to gardeners and commercial fruit growers. It seems peach roots can be a little particular about their soil and are prone to harmful nematodes. Further, I've read that peach can have a short life on its own roots. See
here. I think the reasons listed in that link 1, 4, & 5 could justify grafting specific roots instead of airlayering. After all, bonsai is a long term thing; you'd want the tree to be in good health and more resistant to disease.