Hi VAsleeper,
First of all … congratulations on your new mattress … I think you made a great choice.
As you can see in post #2 here … memory foam (or any all foam mattress) generally does better with a firm non flexing foundation instead of one that has springs in it (I’m assuming here that your box spring has springs) which are generally designed for a mattress that has an innerspring. If the box spring is still in near new condition and has a perfectly flat surface with no soft spots or weak areas (and I would test this by compressing every area of the box spring with your knees) … then it would probably be OK but it may change the designed feel and performance of the mattress to some degree (depending on your weight and on the design and thickness of the mattress).
It may change the feel and performance which for some people may reduce the benefits yes. It would probably be OK as far as the durability of the mattress although I would check with the manufacturer to make sure it fit the criteria of their warranty.
You can read my thoughts about a solid surface platform for a mattress in post #10 here. If you are comfortable with any added risk that comes from lack of ventilation and the plywood was stable on the box spring and didn’t move or sway with your weight on the mattress then it would probably be OK.
It would reduce the risks of poor ventilation between the mattress and the box spring to some degree yes (depending on the size and spacing of the holes).
Phoenix