Not the best idea. A box spring does not have the architectural integrity to support a natural latex mattress.

While you don’t need to use our foundation, we ask that your Spindle be supported properly and have some ventilation. We recommend a support structure with slats that are spaced no more than 3″ apart; there needs to be a rail under the slats running head to foot in the middle, with two supports underneath it that touch the floor; the slats should be at least 3/4″ thick; and the slats are to be made of solid wood and not a composite or plywood like material.

Here are some platform bed options if you need them.
Pompanoosuc Mills Beds
Room Doctor Plateau Platform Bed (If you go with them, do order extra slats. It’s an option that they offer if you ask.) NB: It’s been brought to our attention that the center support on the Room Doctor beds are not supported from the floor. If you use one of these beds we recommend adding at least 1 leg going to the floor.

In the end, we don’t recommend trying to reuse a box spring built for an innerspring mattress. We also suggest you stay away from plywood because of the lack of ventilation, which sometimes can lead to mold or mildew growth on the plywood or mattress.