Never use CDX as an underlayment!
It's full of voids in the plys!
It would be fine to add some screws to what's there now, but I'd never use screws to attach the underlayment.
Reasons being, as a screw goes in it tends to try and lift the underlament before pulling it down, it will leave raised dimples where the head compresses the wood, and voids where the heads of the screws are, it's far slower, and far more expensive.
Keep in mind this needs to be fastened every 4" on the edges, and from 6 to 8" in the field, so that would be a whole lot of screws.
If I did use screws I'd go back over with a random orbital sands, vacuum, then go back and fill all the screw heads so there was no chance the screw heads would mirror through the flooring.
I use a narrow crown staple gun, that way the heads are near invisable.
I've done dozen like this and never once had a call back.