Yes, but I don't know that I would want to deal with a >2 foot wide persimmon. Prepare to split it in half where it falls unless you have a tractor or a boom with a winch. It was arduous trying to move a 6 foot long long 8-10 inches wide from woods to shelter.
It tends to grow very twisted. Does not split easily. Blunts cutting tools some more than others.
Its some pretty mean stuff, and after dealing with the aforementioned persimmon, I would look right past anything larger unless taking it to the saw mill and I wouldn't have a way to get it out of the woods. All that being said persimmon is bow wood, but a wood that won't make anything about it easy for you.
Trees that large might have a decent sized black core. Interesting if sawn, but most if not all would be taken off during shaping the bow. If some could be saved it could make for fine ebony overlays.