Hi cristano,
Yes … if the slats are less than 3" apart then you could use an all latex mattress directly on the slats themselves.
The VOC’s with a bed would typically come from the glue and the finish. Furniture is far from my area of expertise but there are a few options at the end of the foundation post and one of the members has a post here about her bed from tatamiroom which may fit what you are looking for.
Phoenix