just a follow up, i've been reading that propagating from rhizomic shoots is the best way to propagate live oak, would this product still have the same genome as the original tree?

Yes, they'd be genetic clones of the tree they arose from.

You could also graft a scion from the original onto a live oak seedling. I've had great success grafting all members of the white oak group(live oak is in this group), but have not specifically tried live oak - it's not reliably hardy this far north. Grafting oaks is not significantly different than doing fruit trees.