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From personal experience the ply won't give any perceptible reduction in the deflection. Whether or not that's a problem is really going to depend on what you plan to put on them. The set I made with a span of just over a metre needed a centre vertical support to reduce deflection enough for doors underneath when loaded with books, but was fine for open shelving.
±ln(x)
I’m making a couple of torsion box alcove shelves.
2.3m span with 30x30 battens which are fixed together and to studs.
It’s solidly attached but I can flex the middle of the span up and down by 5mm with my hand. Is that going to sort itself out with 12mm ply glued and nailed to top and bottom?
Wondering if I need more spans or worst case some floor braces?