I’ve tried bark grafting old peach wood with very poor results. I would think cleft grafting that stump would yield a low probability of success.
As Alan mentioned, older peach wood doesn’t generate what is called adventitious shoots well. In other words, on some types of trees, if sunlight hits old wood, the wood will start to grow new shoots. For example, if you top an oak tree, lots of new shoot will sprout where it was topped. Likewise, if you cut a hedge tree down, lots of new suckers will come up from the stump.
Peaches tend not to do this. If you don’t see any live buds, peaches tend not to want to throw out new wood from smooth bark, once they get past about 2 years old. Older trees are even worse. I cut down peach trees all the time and rarely see suckers come up from the stump (even from a variety like Redhaven, which puts out lots of renewal wood). Maybe one in ten peach trees I cut down will send up a sucker from the stump. Eastern red cedar trees are the same way.
As Mamuang mentions, it’s a good idea to keep a large sod free area from around the base of a peach tree.