I have successfully grown other palms from seed so I suppose date palms
would do as well. It may be that if yours is the only tree around seeds may
not be viable. In any event I ssupected that seeds from other individual
palm trees may be either all viable or all not viable and I don't know
whether it depends on pollination or the individual tree characteristics.
See the book "Plant Propagation" by the American Horticultural Society (Alan
Toogood, editor--how's that for a monikor) for seed collection and
preparation details.