Hi EZ4HZ,
I don’t know the specifics of your platform bed or the strength or width of the slats but if it has good center support to the floor then it would “probably” be OK for a mattress that has a polyfoam support core. The gaps are a little wide for a mattress that has a latex support core.
For a mattress that has an innerspring support core it would depend on the specifics of the mattress and on the type of innerspring and I would check with the manufacturer of the mattress to confirm that it meets their warranty requirements.
I would also be aware that a support system that flexes will change the feel of your mattress compared to a rigid non flexing support surface (see the posts that are linked in post #22 here).
If the bunkie board or plywood is stable and secure on your platform bed and doesn’t shift or move or make noise when you sleep on it then it would be OK but I would be cautious with a solid surface support system (see post #10 here). I would also make sure that any plywood you use was low VOC (see post #2 here).
There is also more about the types of support systems that are generally best for different types of mattresses in the foundation post here.
Phoenix