Not necessarily, no, because like apples and many other deciduous fruit trees, the seed, if it's produced at all and is actually fertile rather than sterile, does not come true. Seeds of some persimmon trees may be planted and grown by nurseries for use as rootstocks, with the desired variety being grafted onto the rootstock stem. There's not much information in this link https://davesgarden.com/guides/pf/go/149306/ but it does at least confirm that the seeds don't come true. The other link I could provide is to a very long and detailed PDF document published by the Agricultural Department of New South Wales, Australia, where it clearly states they do not come true from seed, but the fact its a PDF and so lengthy deterred me from doing so.