They don't need a graft but persimmons do need male and female trees. This must be a non-native persimmon (which may be grafted to have both male and female branches, I don't know); native persimmons aren't ripe yet.

Hopefully someone can speak from experience. We have the native ones in the neighborhood, but I've not had fruit on mine. I've seen fruit on others nearby though.

Here is a link that might be useful: Persimmons

I have "volunteer" persimmon in my Ellijay (NW Ga) mountain yard. It bears every year. Very prone to fungus (black spot), though.

esh,
Some native persimmons ripen pretty early. I've got one grafted American persimmon variety(NC-10)that's been dropping big, ripe fruits for almost a month now - I've been gathering a gallon ice cream bucket of fruits almost every day since the first week of Sept. The old saw about persimmons not being edible 'til after a frost/freeze is just so much baloney - several of my persimmons will be finished fruiting before we ever get a freeze here.

esther,
For the most part, persimmon trees are either 'male' or 'female' - if you're planting seeds, theoretically 50% will turn out to be fruiting females, 50% non-fruiting males. But - with small numbers, you can't count on the 50/50 thing; I had a friend who planted 6 seeds from a hand-pollenated cross, and got 5 males/1 female. Typically, you'll be waiting 7-10 years for a seedling to reach maturity and begin blooming before you can tell whether you got males or females.
You could plant these seedlings, let them grow for 2-3 years, then graft on scions from trees that produce fruit that you know that you like - then, fruit quality will be a known entity, and grafted trees will usually begin bearing in about half the time(or less) that it takes for a seedling to reach bearing age.

Thanks Lucky for letting me know. I don't have any personal experience with the fruit, so it is good to hear about yours. I'll stop repeating that old saw ... ;).