Can I screw a table base into cured epoxy to attach legs?

No. Cured epoxy, including UltraClear Deep Pour Epoxy, cannot be screwed into. Screwing or drilling into it risks cracking it, so it is not a sound way to mount table legs or a base.

Plan the project so the legs or base attach to the wood, not the epoxy. When you pour over a wood surface, the epoxy bonds directly to the wood, and you can mount that wood however you like. In a river table, the wood slabs on either side of the river are what the base fastens to.

This is also why we do not recommend a table top made of solid epoxy with no wood in it. Epoxy is very heavy, especially in thicker pours, and without a substrate there is no sufficient way to attach legs or support a long, wide span. Epoxy needs a substrate to bond to, or slabs of wood that it connects like a river table. A small charcuterie board can stand alone because of its size and because nothing is drilled into it.

If you do need a hole, make it before the epoxy is applied. Beyond that, how you build and assemble the base is a construction question we are not able to advise on.