Hi Metasequoia,
If I’m understanding you correctly then if the slats are screwed to and resting on the ledge inside the side rails and you end up with a strong, flat, and evenly supportive surface where the gaps between the slats are 3" or less and there is little to no flex in the slats and you have good center support to the floor (in larger sizes) then it would be suitable for a latex mattress yes.
There are also some suggestions that may be helpful to add strength and center support if your bedframe doesn’t have it in post #5 here and the other information it links to.
Phoenix