No chance. I've tried both dormant and non-dormant cuttings with all kinds of techniques including a cloning machine. They are just way to slow to root. It is possible to air-layer them if you are far enough south for them to root during the growing season. There is a technique where a wire is tightened around the scion to build auxin before air layering that I've seen some success with.
Persimmons are easy to start from seed. I've grown seedling using the rootmaker container system and then transplanted them to the field. I have lots of native trees. Grafting them is a much more efficient technique, but they don't always grow where I want them. So, I'll plant a seedling and wait until it is about 1" in diameter and then bark graft it to the variety I want. You an also buy common persimmon seedlings very cheap from many stage agencies. You can plant these and graft them to the desired variety when they get large enough. They don't seem to do as well as the seedling I grow in containers, but it is a lots less work. You can compensate by simply planting more trees than you need, grafting the best when the time comes, and culling the rest.